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Journal articles on the topic 'Completed cohomology'

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Author: Grafiati

Published: 23 September 2022

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1

Blomer, Inga, Peter A. Linnell, and Thomas Schick. "Galois cohomology of completed link groups." Proceedings of the American Mathematical Society 136, no. 10 (May 16, 2008): 3449–59. http://dx.doi.org/10.1090/s0002-9939-08-09395-7.

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2

Barthel, Tobias, and Nathaniel Stapleton. "Brown–Peterson cohomology from Morava -theory." Compositio Mathematica 153, no. 4 (March 13, 2017): 780–819. http://dx.doi.org/10.1112/s0010437x16008241.

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We prove that the $p$-completed Brown–Peterson spectrum is a retract of a product of Morava $E$-theory spectra. As a consequence, we generalize results of Kashiwabara and of Ravenel, Wilson and Yagita from spaces to spectra and deduce that the notion of a good group is determined by Brown–Peterson cohomology. Furthermore, we show that rational factorizations of the Morava $E$-theory of certain finite groups hold integrally up to bounded torsion with height-independent exponent, thereby lifting these factorizations to the rationalized Brown–Peterson cohomology of such groups.

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3

Wu, Yongping, Ying Xu, and Lamei Yuan. "Derivations and Automorphism Group of Completed Witt Lie Algebra." Algebra Colloquium 19, no. 03 (July 5, 2012): 581–90. http://dx.doi.org/10.1142/s1005386712000454.

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In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.

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4

Díaz, Antonio, Albert Ruiz, and Antonio Viruel. "Cohomological uniqueness of some p-groups." Proceedings of the Edinburgh Mathematical Society 56, no. 2 (August 30, 2012): 449–68. http://dx.doi.org/10.1017/s0013091512000247.

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AbstractWe consider classifying spaces of a family of p-groups and prove that mod p cohomology enriched with Bockstein spectral sequences determines their homotopy type among p-completed CW-complexes.

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5

Puig, Lluis. "Existence, Uniqueness and Functoriality of the Perfect Locality over a Frobenius P-Category." Algebra Colloquium 23, no. 04 (September 26, 2016): 541–622. http://dx.doi.org/10.1142/s1005386716000523.

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Let p be a prime, P a finite p-group and ℱ a Frobenius P-category. The question on the existence of a suitable category ℒ sc extending the full subcategory of ℱ over the set of ℱ-selfcentralizing subgroups of P goes back to Dave Benson in 1994. In 2002 Carles Broto, Ran Levi and Bob Oliver formulate the existence and the uniqueness of the category ℒ sc in terms of the annulation of an obstruction 3 -cohomology element and of the vanishing of a 2-cohomology group, and they state a sufficient condition for the vanishing of these n-cohomology groups. Recently, Andrew Chermak has proved the existence and the uniqueness of ℒ sc via his objective partial groups, and Bob Oliver, following some of Chermak's methods, has also proved the vanishing of those n-cohomology groups for n > 1, both applying the Classification of the finite simple groups. Here we give direct proofs of the existence and the uniqueness of ℒ sc ; moreover, in [11] we already show that ℒ sc can be completed in a suitable category ℒ extending ℱ and we also prove some functoriality of this correspondence.

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6

Newton, James. "Completed cohomology of Shimura curves and a p-adic Jacquet–Langlands correspondence." Mathematische Annalen 355, no. 2 (March 10, 2012): 729–63. http://dx.doi.org/10.1007/s00208-012-0796-y.

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7

Dotto, Andrea, and Daniel Le. "Diagrams in the mod p cohomology of Shimura curves." Compositio Mathematica 157, no. 8 (July 7, 2021): 1653–723. http://dx.doi.org/10.1112/s0010437x21007375.

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AbstractWe prove a local–global compatibility result in the mod $p$ Langlands program for $\mathrm {GL}_2(\mathbf {Q}_{p^f})$. Namely, given a global residual representation $\bar {r}$ appearing in the mod $p$ cohomology of a Shimura curve that is sufficiently generic at $p$ and satisfies a Taylor–Wiles hypothesis, we prove that the diagram occurring in the corresponding Hecke eigenspace of mod $p$ completed cohomology is determined by the restrictions of $\bar {r}$ to decomposition groups at $p$. If these restrictions are moreover semisimple, we show that the $(\varphi ,\Gamma )$-modules attached to this diagram by Breuil give, under Fontaine's equivalence, the tensor inductions of the duals of the restrictions of $\bar {r}$ to decomposition groups at $p$.

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8

Isaksen, Daniel C., and Armira Shkembi. "Motivic connective K-theories and the cohomology of A(1)." Journal of K-theory 7, no. 3 (May 24, 2011): 619–61. http://dx.doi.org/10.1017/is011004009jkt154.

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AbstractWe make some computations in stable motivic homotopy theory over Spec ℂ, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct over ℂ a motivic analogue of the real K-theory spectrum KO. We also establish a theory of motivic connective covers over ℂ to obtain a motivic version of ko. We establish an Adams spectral sequence for computing motivic ko-homology. The E2-term of this spectral sequence involves Ext groups over the subalgebra A(1) of the motivic Steenrod algebra. We make several explicit computations of these E2-terms in interesting special cases.

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9

Asadollahi, Javad, and Shokrollah Salarian. "Complete Cohomologies and Some Homological Invariants." Algebra Colloquium 14, no. 01 (March 2007): 155–66. http://dx.doi.org/10.1142/s1005386707000156.

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There is a complete cohomology theory developed over a commutative noetherian ring in which injectives take the role of projectives in Vogel's construction of complete cohomology theory. We study the interaction between this complete cohomology, that is referred to as [Formula: see text]-complete cohomology, and Vogel's one and give some sufficient conditions for their equivalence. Using [Formula: see text]-complete functors, we assign a new homological invariant to any finitely generated module over an arbitrary commutative noetherian local ring, that would generalize Auslander's delta invariant. We generalize the results about the δ-invariant to arbitrary rings and give a sufficient condition for the vanishing of this new invariant. We also introduce an analogue of the notion of the index of a Gorenstein local ring, introduced by Auslander, for arbitrary local rings and study its behavior under flat extensions of local rings. Finally, we study the connection between the index and Loewy length of a local ring and generalize the main result of [11] to arbitrary rings.

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10

Emmanouil, Ioannis. "Balance in complete cohomology." Journal of Pure and Applied Algebra 218, no. 4 (April 2014): 618–23. http://dx.doi.org/10.1016/j.jpaa.2013.08.001.

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11

Hu, Jiangsheng, Dongdong Zhang, Tiwei Zhao, and Panyue Zhou. "Complete Cohomology for Extriangulated Categories." Algebra Colloquium 28, no. 04 (November 8, 2021): 701–20. http://dx.doi.org/10.1142/s1005386721000547.

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Let [Formula: see text] be an extriangulated category with a proper class [Formula: see text] of [Formula: see text]-triangles. We study complete cohomology of objects in [Formula: see text] by applying [Formula: see text]-projective resolutions and [Formula: see text]-injective coresolutions constructed in [Formula: see text]. Vanishing of complete cohomology detects objects with finite [Formula: see text]-projective dimension and finite [Formula: see text]-injective dimension. As a consequence, we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein. Moreover, we give a general technique for computing complete cohomology of objects with finite [Formula: see text]-[Formula: see text]projective dimension. As an application, the relations between [Formula: see text]-projective dimension and [Formula: see text]-[Formula: see text]projective dimension for objects in [Formula: see text] are given.

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12

Erdmann, Karin, and Magnus Hellstrøm-Finnsen. "Hochschild cohomology of some quantum complete intersections." Journal of Algebra and Its Applications 17, no. 11 (November 2018): 1850215. http://dx.doi.org/10.1142/s0219498818502158.

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We compute the Hochschild cohomology ring of the algebras [Formula: see text] over a field [Formula: see text] where [Formula: see text] and where [Formula: see text] is a primitive [Formula: see text]th root of unity. We find the dimension of [Formula: see text] and show that it is independent of [Formula: see text]. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

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13

Dembegioti, Fotini. "On the zeroeth complete cohomology." Journal of Pure and Applied Algebra 203, no. 1-3 (December 2005): 119–32. http://dx.doi.org/10.1016/j.jpaa.2005.03.008.

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14

Dimca, Alexandru. "Residues and cohomology of complete intersections." Duke Mathematical Journal 78, no. 1 (April 1995): 89–100. http://dx.doi.org/10.1215/s0012-7094-95-07805-3.

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15

Aleksandrov, A. G. "COHOMOLOGY OF A QUASIHOMOGENEOUS COMPLETE INTERSECTION." Mathematics of the USSR-Izvestiya 26, no. 3 (June 30, 1986): 437–77. http://dx.doi.org/10.1070/im1986v026n03abeh001155.

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16

SUWA, Noriyuki. "Hodge-Witt cohomology of complete intersections." Journal of the Mathematical Society of Japan 45, no. 2 (April 1993): 295–300. http://dx.doi.org/10.2969/jmsj/04520295.

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17

Lu, H., C. N. Pope, X. J. Wang, and K. W. Xu. "The complete cohomology of the string." Classical and Quantum Gravity 11, no. 4 (April 1, 1994): 967–81. http://dx.doi.org/10.1088/0264-9381/11/4/013.

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18

Mazzeo, Rafe, Álvaro Pelayo, and Tudor S. Ratiu. "L2-cohomology and complete Hamiltonian manifolds." Journal of Geometry and Physics 87 (January 2015): 305–13. http://dx.doi.org/10.1016/j.geomphys.2014.07.012.

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19

Asadollahi, J., F. Jahanshahi, and Sh Salarian. "Complete cohomology and Gorensteinness of schemes." Journal of Algebra 319, no. 6 (March 2008): 2626–51. http://dx.doi.org/10.1016/j.jalgebra.2007.11.020.

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20

Huyghe, Christine, and Tobias Schmidt. "𝒟-modules arithmétiques sur la variété de drapeaux." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 754 (September 1, 2019): 1–15. http://dx.doi.org/10.1515/crelle-2017-0021.

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Abstract Soient p un nombre premier, V un anneau de valuation discrète complet d’inégales caractéristiques (0,p) , et G un groupe réductif et deployé sur \operatorname{Spec}V . Nous obtenons un théorème de localisation, en utilisant les distributions arithmétiques, pour le faisceau des opérateurs différentiels arithmétiques sur la variété de drapeaux formelle de G. Nous donnons une application à la cohomologie rigide pour des ouverts dans la variété de drapeaux en caractéristique p. Let p be a prime number, V a complete discrete valuation ring of unequal characteristics (0,p) , and G a connected split reductive algebraic group over \operatorname{Spec}V . We obtain a localization theorem, involving arithmetic distributions, for the sheaf of arithmetic differential operators on the formal flag variety of G. We give an application to the rigid cohomology of open subsets in the characteristic p flag variety.

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21

Zhongkui, Liu, and Xie Zongyang. "Relative cohomology of complexes based on cotorsion pairs." Journal of Algebra and Its Applications 19, no. 05 (May 21, 2019): 2050092. http://dx.doi.org/10.1142/s0219498820500929.

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Let [Formula: see text] be an associative ring with identity. The purpose of this paper is to establish relative cohomology theories based on cotorsion pairs in the setting of unbounded complexes of modules over [Formula: see text]. Let [Formula: see text] be a complete hereditary cotorsion pair in [Formula: see text]-Mod. Then [Formula: see text] and [Formula: see text] are complete hereditary cotorsion pairs in the category of [Formula: see text]-complexes. For any complexes [Formula: see text] and [Formula: see text] and any [Formula: see text], we define the [Formula: see text]th relative cohomology groups [Formula: see text] and [Formula: see text] by special [Formula: see text]-precovers of [Formula: see text] and by special [Formula: see text]-preenvelopes of [Formula: see text], respectively. They are common generalizations of absolute cohomology groups and Gorenstein cohomology groups of complexes. Some induced exact sequences concerning relative cohomology groups are considered. It is also shown that the relative cohomology functor of complexes we considered is balanced.

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22

Qian, Zicheng. "Dilogarithm and higher ℒ-invariants for 𝒢ℒ₃(𝐐_{𝐩})." Representation Theory of the American Mathematical Society 25, no. 12 (May 3, 2021): 344–411. http://dx.doi.org/10.1090/ert/567.

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The primary purpose of this paper is to clarify the relation between previous results in [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145], [Amer. J. Math. 141 (2019), pp. 661–703], and [Camb. J. Math. 8 (2020), p. 775–951] via the construction of some interesting locally analytic representations. Let E E be a sufficiently large finite extension of Q p \mathbf {Q}_p and ρ p \rho _p be a p p -adic semi-stable representation G a l ( Q p ¯ / Q p ) → G L 3 ( E ) \mathrm {Gal}(\overline {\mathbf {Q}_p}/\mathbf {Q}_p)\rightarrow \mathrm {GL}_3(E) such that the associated Weil–Deligne representation W D ( ρ p ) \mathrm {WD}(\rho _p) has rank two monodromy and the associated Hodge filtration is non-critical. A computation of extensions of rank one ( φ , Γ ) (\varphi , \Gamma ) -modules shows that the Hodge filtration of ρ p \rho _p depends on three invariants in E E . We construct a family of locally analytic representations Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) of G L 3 ( Q p ) \mathrm {GL}_3(\mathbf {Q}_p) depending on three invariants L 1 , L 2 , L 3 ∈ E \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3 \in E , such that each representation in the family contains the locally algebraic representation A l g ⊗ S t e i n b e r g \mathrm {Alg}\otimes \mathrm {Steinberg} determined by W D ( ρ p ) \mathrm {WD}(\rho _p) (via classical local Langlands correspondence for G L 3 ( Q p ) \mathrm {GL}_3(\mathbf {Q}_p) ) and the Hodge–Tate weights of ρ p \rho _p . When ρ p \rho _p comes from an automorphic representation π \pi of a unitary group over Q \mathbf {Q} which is compact at infinity, we show (under some technical assumption) that there is a unique locally analytic representation in the above family that occurs as a subrepresentation of the Hecke eigenspace (associated with π \pi ) in the completed cohomology. We note that [Amer. J. Math. 141 (2019), pp. 611–703] constructs a family of locally analytic representations depending on four invariants ( cf. (4) in that publication ) and proves that there is a unique representation in this family that embeds into the Hecke eigenspace above. We prove that if a representation Π \Pi in Breuil’s family embeds into the Hecke eigenspace above, the embedding of Π \Pi extends uniquely to an embedding of a Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) into the Hecke eigenspace, for certain L 1 , L 2 , L 3 ∈ E \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3\in E uniquely determined by Π \Pi . This gives a purely representation theoretical necessary condition for Π \Pi to embed into completed cohomology. Moreover, certain natural subquotients of Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) give an explicit complex of locally analytic representations that realizes the derived object Σ ( λ , L _ ) \Sigma (\lambda , \underline {\mathscr {L}}) in (1.14) of [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145]. Consequently, the locally analytic representation Σ m i n ( λ , L 1 , L 2 , L 3 ) \Sigma ^{\mathrm {min}}(\lambda , \mathscr {L}_1, \mathscr {L}_2, \mathscr {L}_3) gives a relation between the higher L \mathscr {L} -invariants studied in [Amer. J. Math. 141 (2019), pp. 611–703] as well as the work of Breuil and Ding and the p p -adic dilogarithm function which appears in the construction of Σ ( λ , L _ ) \Sigma (\lambda , \underline {\mathscr {L}}) in [Ann. Sci. Éc. Norm. Supér. 44 (2011), pp. 43–145].

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23

Coltoiu, Mihnea. "On Barth’s conjecture concerining." Nagoya Mathematical Journal 145 (March 1997): 99–123. http://dx.doi.org/10.1017/s0027763000006127.

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A classical, still unsolved problem, is the following: is every connected curve A ⊂ P3 a set-theoretic complete intersection? It is clear that if A is a set-theoretic complete intersection then:a) The algebraic cohomology groups vanish for every coherent algebraic sheaf on P3.b) The analytic cohomology groups vanish for every coherent analytic sheaf on P3\A.

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24

Kim, Jin Hong. "On the integral cohomology of toric varieties." Journal of Algebra and Its Applications 15, no. 02 (October 6, 2015): 1650032. http://dx.doi.org/10.1142/s0219498816500328.

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It is known that the integral cohomology algebra of any smooth compact toric variety XΣ associated to a complete regular fan Σ is isomorphic to the Stanley–Reisner algebra ℤ[Σ] modulo the ideal JΣ generated by linear relations determined by Σ. The aim of this paper is to show how to determine the integral cohomology algebra of a toric variety (in particular, a projective toric variety) associated to a certain simplicial fan. As a consequence, we confirm our expectation that for a certain simplicial fan the integral cohomology algebra is also given by the same formula as in a complete regular fan.

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25

Nucinkis, Brita E. A. "Complete cohomology for arbitrary rings using injectives." Journal of Pure and Applied Algebra 131, no. 3 (October 1998): 297–318. http://dx.doi.org/10.1016/s0022-4049(97)00082-0.

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26

Bergh, Petter, and Karin Erdmann. "Homology and cohomology of quantum complete intersections." Algebra & Number Theory 2, no. 5 (July 4, 2008): 501–22. http://dx.doi.org/10.2140/ant.2008.2.501.

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27

SADEGHI, ARASH. "VANISHING OF COHOMOLOGY OVER COMPLETE INTERSECTION RINGS." Glasgow Mathematical Journal 57, no. 2 (December 18, 2014): 445–55. http://dx.doi.org/10.1017/s0017089514000408.

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AbstractLet R be a complete intersection ring, and let M and N be R-modules. It is shown that the vanishing of ExtiR(M, N) for a certain number of consecutive values of i starting at n forces the complete intersection dimension of M to be at most n–1. We also estimate the complete intersection dimension of M*, the dual of M, in terms of vanishing of cohomology modules, ExtiR(M,N).

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28

TALELLI, OLYMPIA. "PERIODICITY IN GROUP COHOMOLOGY AND COMPLETE RESOLUTIONS." Bulletin of the London Mathematical Society 37, no. 04 (August 2005): 547–54. http://dx.doi.org/10.1112/s0024609305004273.

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29

Angella, Daniele, and Simone Calamai. "Bott–Chern cohomology and q-complete domains." Comptes Rendus Mathematique 351, no. 9-10 (May 2013): 343–48. http://dx.doi.org/10.1016/j.crma.2013.05.006.

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30

Avramov, Luchezar L., and Ragnar-Olaf Buchweitz. "Support varieties and cohomology over complete intersections." Inventiones Mathematicae 142, no. 2 (November 1, 2000): 285–318. http://dx.doi.org/10.1007/s002220000090.

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31

Funar, Louis. "On the cohomology of weighted complete intersections." Archiv der Mathematik 63, no. 6 (December 1994): 497–99. http://dx.doi.org/10.1007/bf01202064.

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32

Mavlyutov, Anvar R. "Cohomology of complete intersections in toric varieties." Pacific Journal of Mathematics 191, no. 1 (November 1, 1999): 133–44. http://dx.doi.org/10.2140/pjm.1999.191.133.

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33

KYED, DAVID, and HENRIK DENSING PETERSEN. "POLYNOMIAL COHOMOLOGY AND POLYNOMIAL MAPS ON NILPOTENT GROUPS." Glasgow Mathematical Journal 62, no. 3 (October 2, 2019): 706–36. http://dx.doi.org/10.1017/s0017089519000429.

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AbstractWe introduce a refined version of group cohomology and relate it to the space of polynomials on the group in question. We show that the polynomial cohomology with trivial coefficients admits a description in terms of ordinary cohomology with polynomial coefficients, and that the degree one polynomial cohomology with trivial coefficients admits a description directly in terms of polynomials. Lastly, we give a complete description of the polynomials on a connected, simply connected nilpotent Lie group by showing that these are exactly the maps that pull back to classical polynomials via the exponential map.

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34

Zhou, Jian, and Xiaobo Zhuang. "Witten genus of generalized complete intersections in products of Grassmannians." International Journal of Mathematics 25, no. 10 (September 2014): 1450095. http://dx.doi.org/10.1142/s0129167x14500955.

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35

Katok, Anatole, and Svetlana Katok. "Higher cohomology for Abelian groups of toral automorphisms." Ergodic Theory and Dynamical Systems 15, no. 3 (June 1995): 569–92. http://dx.doi.org/10.1017/s0143385700008531.

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AbstractWe give a complete description of smooth untwisted cohomology with coefficients in ℝl for ℤk-actions by hyperbolic automorphisms of a torus. For 1 ≤ n ≤ k − 1 the nth cohomology trivializes, i.e. every cocycle is cohomologous to a constant cocycle via a smooth coboundary. For n = k a counterpart of the classical Livshitz Theorem holds: the cohomology class of a smooth k-cocycle is determined by periodic data.

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36

Vâjâitu, Viorel. "Cohomology Groups of Locally $q$-Complete Morphisms with $r$-Complete Base." MATHEMATICA SCANDINAVICA 79 (June 1, 1996): 161. http://dx.doi.org/10.7146/math.scand.a-12598.

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37

Zhuang, Xiaobo. "Vanishing theorems of generalized Witten genus for generalized complete intersections in flag manifolds." International Journal of Mathematics 27, no. 09 (August 2016): 1650076. http://dx.doi.org/10.1142/s0129167x16500762.

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We propose a potential function [Formula: see text] for the cohomology ring of partial flag manifolds. We prove a formula expressing integrals over partial flag manifolds by residues, which generalizes [E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, in Geometry, Topology, Physics (International Press, 1995), pp. 357–422]. Using this formula, we prove a Landweber–Stong type vanishing theorem for generalized [Formula: see text] complete intersections in flag manifolds, which serves as evidence for the [Formula: see text] version of Stolz conjecture [Q. Chen, F. Han and W. Zhang, Generalized Witten genus and vanishing theorems, J. Differential Geom. 88(1) (2011) 1–39].

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38

Lykova, Zinaida A. "Hochschild cohomology of tensor products of topological algebras." Proceedings of the Edinburgh Mathematical Society 53, no. 2 (April 30, 2010): 447–70. http://dx.doi.org/10.1017/s0013091508001065.

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AbstractWe describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of $\widehat{\otimes}$-algebras which are Fréchet spaces or nuclear DF-spaces. To this end we establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF-complexes and in the Künneth formula for continuous Hochschild cohomology of nuclear $\widehat{\otimes}$-algebras which are Fréchet spaces or DF-spaces for which all boundary maps of the standard homology complexes have closed ranges.

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39

Nozawa, Takeshi. "On the complete relative cohomology of Frobenius extensions." Tsukuba Journal of Mathematics 17, no. 1 (June 1993): 99–113. http://dx.doi.org/10.21099/tkbjm/1496162133.

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40

Oppermann, Steffen. "Hochschild cohomology and homology of quantum complete intersections." Algebra & Number Theory 4, no. 7 (December 31, 2010): 821–38. http://dx.doi.org/10.2140/ant.2010.4.821.

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41

Alaoui, Youssef. "Cohomology of locallyq-complete sets in Stein manifolds." Complex Variables and Elliptic Equations 51, no. 2 (February 2006): 137–41. http://dx.doi.org/10.1080/02781070500397660.

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42

Judson, Thomas W. "Complete filtered Lie algebras and the Spencer cohomology." Journal of Algebra 125, no. 1 (August 1989): 66–109. http://dx.doi.org/10.1016/0021-8693(89)90294-9.

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43

Beauville, Arnaud. "The primitive cohomology lattice of a complete intersection." Comptes Rendus Mathematique 347, no. 23-24 (December 2009): 1399–402. http://dx.doi.org/10.1016/j.crma.2009.10.013.

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44

Christensen, Erik, Edward G. Effros, and Allan Sinclair. "Completely bounded multilinear maps andC *-algebraic cohomology." Inventiones Mathematicae 90, no. 2 (June 1987): 279–96. http://dx.doi.org/10.1007/bf01388706.

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45

Linckelmann, Markus. "Integrable Derivations and Stable Equivalences of Morita Type." Proceedings of the Edinburgh Mathematical Society 61, no. 2 (February 15, 2018): 343–62. http://dx.doi.org/10.1017/s0013091517000098.

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AbstractUsing that integrable derivations of symmetric algebras can be interpreted in terms of Bockstein homomorphisms in Hochschild cohomology, we show that integrable derivations are invariant under the transfer maps in Hochschild cohomology of symmetric algebras induced by stable equivalences of Morita type. With applications in block theory in mind, we allow complete discrete valuation rings of unequal characteristic.

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46

DeLand, Matthew. "Complete Families of Linearly Non-degenerate Rational Curves." Canadian Mathematical Bulletin 54, no. 3 (September 1, 2011): 430–41. http://dx.doi.org/10.4153/cmb-2011-021-2.

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AbstractWe prove that every complete family of linearly non-degenerate rational curves of degree e > 2 in ℙn has atmost n–1 moduli. For e = 2 we prove that such a family has at most n moduli. The general method involves exhibiting a map from the base of a family X to the Grassmannian of e-planes in ℙn and analyzing the resulting map on cohomology.

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CIOLLI, GIANNI. "ON THE QUANTUM COHOMOLOGY OF SOME FANO THREEFOLDS AND A CONJECTURE OF DUBROVIN." International Journal of Mathematics 16, no. 08 (September 2005): 823–39. http://dx.doi.org/10.1142/s0129167x05003144.

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In the present paper the small quantum cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from ℙ3or the quadric Q3is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov–Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of quantum cohomology is proven by checking the computed quantum cohomology rings and by showing that a smooth Fano threefold X with b3(X) = 0 admits a complete exceptional set of the appropriate length.

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48

Tsuji, Takeshi. "On nearby cycles and 𝒟-modules of log schemes in characteristic p>0." Compositio Mathematica 146, no. 6 (June 16, 2010): 1552–616. http://dx.doi.org/10.1112/s0010437x10004768.

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AbstractLet K be a complete discrete valuation field of mixed characteristic (0,p) with a perfect residue field k. For a semi-stable scheme over the ring of integers OK of K or, more generally, for a log smooth scheme of semi-stable type over k, we define nearby cycles as a single 𝒟-module endowed with a monodromy ∂logt, whose cohomology should give the log crystalline cohomology. We also explicitly describe the monodromy filtration of the 𝒟-module with respect to the endomorphism ∂logt, and construct a weight spectral sequence for the cohomology of the nearby cycles.

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PETROVIĆ, ZORAN Z., and BRANISLAV I. PRVULOVIĆ. "ON GRÖBNER BASES FOR FLAG MANIFOLDS F(1, 1, … , 1, n)." Journal of Algebra and Its Applications 12, no. 03 (December 20, 2012): 1250182. http://dx.doi.org/10.1142/s0219498812501824.

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The knowledge of cohomology of a manifold has shown to be quite relevant in various investigations: the question of vector fields, immersion and embedding dimension, and recently even in topological robotics. The method of Gröbner bases is applicable when the cohomology of the manifold is a quotient of a polynomial algebra. The mod 2 cohomology of the real flag manifold F(n1, n2, …, nr) is known to be isomorphic to a polynomial algebra modulo a certain ideal. Reduced Gröbner bases for these ideals are obtained in the case of manifolds F(1, 1, …, 1, n) including the complete flag manifolds (n = 1).

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Goertsches, Oliver, and Dirk Töben. "Equivariant basic cohomology of Riemannian foliations." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 745 (December 1, 2018): 1–40. http://dx.doi.org/10.1515/crelle-2015-0102.

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Abstract The basic cohomology of a complete Riemannian foliation with all leaves closed is the cohomology of the leaf space. In this paper we introduce various methods to compute the basic cohomology in the presence of both closed and non-closed leaves in the simply-connected case (or more generally for Killing foliations): We show that the total basic Betti number of the union C of the closed leaves is smaller than or equal to the total basic Betti number of the foliated manifold, and we give sufficient conditions for equality. If there is a basic Morse–Bott function with critical set equal to C, we can compute the basic cohomology explicitly. Another case in which the basic cohomology can be determined is if the space of leaf closures is a simple, convex polytope. Our results are based on Molino’s observation that the existence of non-closed leaves yields a distinguished transverse action on the foliated manifold with fixed point set C. We introduce equivariant basic cohomology of transverse actions in analogy to equivariant cohomology of Lie group actions enabling us to transfer many results from the theory of Lie group actions to Riemannian foliations. The prominent role of the fixed point set in the theory of torus actions explains the relevance of the set C in the basic setting.

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