Добірка наукової літератури з теми "Faltings annihilator theorem"

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Статті в журналах з теми "Faltings annihilator theorem"

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Kawasaki, Takesi. "On Faltings' annihilator theorem." Proceedings of the American Mathematical Society 136, no. 04 (November 23, 2007): 1205–11. http://dx.doi.org/10.1090/s0002-9939-07-09128-9.

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Doustimehr, Mohammad Reza, and Reza Naghipour. "On the generalization of Faltings’ Annihilator Theorem." Archiv der Mathematik 102, no. 1 (January 2014): 15–23. http://dx.doi.org/10.1007/s00013-013-0601-5.

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Doustimehr, Mohammad Reza. "Faltings’ local–global principle and annihilator theorem for the finiteness dimensions." Communications in Algebra 47, no. 5 (February 20, 2019): 1853–61. http://dx.doi.org/10.1080/00927872.2018.1523423.

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Sharp, Rodney Y. "Bass Numbers in the Graded Case, a-Invariant Formulas, and an Analogue of Faltings' Annihilator Theorem." Journal of Algebra 222, no. 1 (December 1999): 246–70. http://dx.doi.org/10.1006/jabr.1999.8013.

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Divaani-Aazar, Kamran, and Majid Rahro Zargar. "The derived category analogues of Faltings Local-global Principle and Annihilator Theorems." Journal of Algebra and Its Applications 18, no. 07 (July 2019): 1950140. http://dx.doi.org/10.1142/s0219498819501408.

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Let [Formula: see text] be a specialization closed subset of Spec R and X a homologically left-bounded complex with finitely generated homologies. We establish Faltings’ Local-global Principle and Annihilator Theorems for the local cohomology modules [Formula: see text] Our versions contain variations of results already known on these theorems.
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Khashyarmanesh, K., and Sh Salarian. "Faltings' theorem for the annihilation of local cohomology modules over a Gorenstein ring." Proceedings of the American Mathematical Society 132, no. 08 (August 1, 2004): 2215. http://dx.doi.org/10.1090/s0002-9939-04-07322-8.

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Дисертації з теми "Faltings annihilator theorem"

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Martini, Lorenzo. "Local coherence of hearts in the derived category of a commutative ring." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/354322.

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Approximation theory is a fundamental tool in order to study the representation theory of a ring R. Roughly speaking, it consists in determining suitable additive or abelian subcategories of the whole module category Mod-R with nice enough functorial properties. For example, torsion theory is a well suited incarnation of approximation theory. Of course, such an idea has been generalised to the additive setting itself, so that both Mod-R and other interesting categories related with R may be linked functorially. By the seminal work of Beilinson, Bernstein and Deligne (1982), the derived category of the ring turns out to admit useful torsion theories, called t-structures: they are pairs of full subcategories of D(R) whose intersection, called the heart, is always an abelian category. The so-called standard t-structure of D(R) has as its heart the module category Mod-R itself. Since then a lot of results devoted to the module theoretic characterisation of the hearts have been achieved, providing evidence of the usefulness of the t-structures in the representation theory of R. In 2020, following a research line promoted by many other authors, Saorin and Stovicek proved that the heart of any compactly generated t-structure is always a locally finitely presented Grothendieck categories (actually, this is true for any t-structure in a triangulated category with coproducts). Essentially, this means that the hearts of D(R) come equipped with a finiteness condition miming that one valid in Mod-R. In the present thesis we tackle the problem of characterising when the hearts of certain compactly generated t-structures of a commutative ring are even locally coherent. In this commutative context, after the works of Neeman and Alonso, Jeremias and Saorin, compactly generated t-structures turned out to be very interesting over a noetherian ring, for they are in bijection with the Thomason filtrations of the prime spectrum. In other words, they are classified by geometric objects, moreover their constituent subcategories have a precise cohomological description. However, if the ascending chain condition lacks, such classification is somehow partial, though provided by Hrbek. The crucial point is that the constituents of the t-structures have a different description w.r.t. that available in the noetherian setting, yet if one copies the latter for an arbitrary ring still obtains a t-structure, but it is not clear whether it must be compactly generated. Consequently, pursuing the study of the local coherence of the hearts given by a Thomason filtration, we ended by considering two t-structures. Our technique in order to face the lack of the ascending chain condition relies on a further approximation of the hearts by means of suitable torsion theories. The main results of the thesis are the following: we prove that for the so-called weakly bounded below Thomason filtrations the two t-structures have the same heart (therefore it is always locally finitely presented), and we show that they coincide if and only they are both compactly generated. Moreover, we achieve a complete characterisation of the local coherence for the hearts of the Thomason filtrations of finite length.
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