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Journal articles on the topic 'Cohomologie completée'

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Published: 23 September 2022

Last updated: 4 November 2022

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1

Déglise, F., and N. Mazzari. "THE RIGID SYNTOMIC RING SPECTRUM." Journal of the Institute of Mathematics of Jussieu 14, no. 4 (June 13, 2014): 753–99. http://dx.doi.org/10.1017/s1474748014000152.

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The aim of this paper is to show that rigid syntomic cohomology – defined by Besser – is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous constructions, we exhibit a simple representability criterion and we apply it to several cohomologies in order to get our central result. This theorem gives new results for rigid syntomic cohomology such as h-descent and the compatibility of cycle classes with Gysin morphisms. Along the way, we prove that motivic ring spectra induce a complete Bloch–Ogus cohomological formalism and even more. Finally, following a general motivic homotopical philosophy, we exhibit a natural notion of rigid syntomic coefficients.

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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

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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34

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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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

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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37

Luecke, Kiran. "Completed K-theory and equivariant elliptic cohomology." Advances in Mathematics 410 (December 2022): 108754. http://dx.doi.org/10.1016/j.aim.2022.108754.

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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

Calmès, Baptiste, Viktor Petrov, and Kirill Zainoulline. "Invariants, torsion indices and oriented cohomology of complete flags." Annales scientifiques de l'École normale supérieure 46, no. 3 (2013): 405–48. http://dx.doi.org/10.24033/asens.2192.

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40

Donnelly, Harold. "$L_2$ cohomology of pseudoconvex domains with complete Kähler metric." Michigan Mathematical Journal 41, no. 3 (1994): 433–42. http://dx.doi.org/10.1307/mmj/1029005071.

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41

Tran, Nghia T. H., and Emil Sköldberg. "The Hochschild cohomology of square-free monomial complete intersections." Communications in Algebra 47, no. 8 (February 10, 2019): 3040–55. http://dx.doi.org/10.1080/00927872.2018.1549665.

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42

Esnault, Hélène, and Daqing Wan. "Hodge type of the exotic cohomology of complete intersections." Comptes Rendus Mathematique 336, no. 2 (January 2003): 153–57. http://dx.doi.org/10.1016/s1631-073x(03)00013-x.

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43

Patyi, Imre. "Analytic cohomology of complete intersections in a Banach space." Annales de l’institut Fourier 54, no. 1 (2004): 147–58. http://dx.doi.org/10.5802/aif.2013.

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44

Roe, John. "Coarse cohomology and index theory on complete Riemannian manifolds." Memoirs of the American Mathematical Society 104, no. 497 (1993): 0. http://dx.doi.org/10.1090/memo/0497.

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45

Dembegioti, Fotini. "On the Zeroeth Complete Cohomology of Certain Polycyclic Groups." Communications in Algebra 36, no. 5 (May 15, 2008): 1927–41. http://dx.doi.org/10.1080/00927870801941622.

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46

Yu, G. L. "Cyclic Cohomology and Higher Indexes for Noncompact Complete Manifolds." Journal of Functional Analysis 133, no. 2 (November 1995): 442–73. http://dx.doi.org/10.1006/jfan.1995.1133.

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47

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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48

Switala, Nicholas. "On the de Rham homology and cohomology of a complete local ring in equicharacteristic zero." Compositio Mathematica 153, no. 10 (August 7, 2017): 2075–146. http://dx.doi.org/10.1112/s0010437x17007345.

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Let $A$ be a complete local ring with a coefficient field $k$ of characteristic zero, and let $Y$ be its spectrum. The de Rham homology and cohomology of $Y$ have been defined by R. Hartshorne using a choice of surjection $R\rightarrow A$ where $R$ is a complete regular local $k$-algebra: the resulting objects are independent of the chosen surjection. We prove that the Hodge–de Rham spectral sequences abutting to the de Rham homology and cohomology of $Y$, beginning with their $E_{2}$-terms, are independent of the chosen surjection (up to a degree shift in the homology case) and consist of finite-dimensional $k$-spaces. These $E_{2}$-terms therefore provide invariants of $A$ analogous to the Lyubeznik numbers. As part of our proofs we develop a theory of Matlis duality in relation to ${\mathcal{D}}$-modules that is of independent interest. Some of the highlights of this theory are that if $R$ is a complete regular local ring containing $k$ and ${\mathcal{D}}={\mathcal{D}}(R,k)$ is the ring of $k$-linear differential operators on $R$, then the Matlis dual $D(M)$ of any left ${\mathcal{D}}$-module $M$ can again be given a structure of left ${\mathcal{D}}$-module, and if $M$ is a holonomic ${\mathcal{D}}$-module, then the de Rham cohomology spaces of $D(M)$ are $k$-dual to those of $M$.

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49

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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50

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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