-cohomology
J. Eichhorn (1986)
Banach Center Publications
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J. Eichhorn (1986)
Banach Center Publications
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Christopher Davis, Andreas Langer, Thomas Zink (2011)
Annales scientifiques de l'École Normale Supérieure
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The goal of this work is to construct, for a smooth variety over a perfect field k of finite characteristic , an overconvergent de Rham-Witt complex as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in , is a complex of étale sheaves and a differential graded algebra over the ring of overconvergent Witt-vectors. If is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...
Bruno Kahn, R. Sujatha (2000)
Journal of the European Mathematical Society
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This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension and . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real...
Marc Burger, Nicolas Monod (1999)
Journal of the European Mathematical Society
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We prove that the natural map from bounded to usual cohomology is injective if is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for : the stable commutator length vanishes and any –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating to the continuous bounded cohomology of the...
J. Asadollahi, K. Khashyarmanesh, Sh. Salarian (2001)
Colloquium Mathematicae
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Let A be a Noetherian ring, let M be a finitely generated A-module and let Φ be a system of ideals of A. We prove that, for any ideal in Φ, if, for every prime ideal of A, there exists an integer k(), depending on , such that kills the general local cohomology module for every integer j less than a fixed integer n, where , then there exists an integer k such that for every j < n.
Tom Coates, Yongbin Ruan (2013)
Annales de l’institut Fourier
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We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold to the quantum cohomology of a crepant resolution of . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines...
Nicola Pagani (2013)
Annales de l’institut Fourier
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In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable -pointed curves of genus . In the first part of the paper we study and describe stack theoretically the twisted sectors of and . In the second part, we study the orbifold intersection theory of . We suggest a definition for an orbifold tautological ring in genus , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.
Bo Hou, Yanhong Guo (2015)
Czechoslovak Mathematical Journal
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The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let be the Yoneda algebra of a reconstruction algebra of type over a field t-dimensions of all Hochschild homology and cohomology groups of are calculated explicitly.
A. A. Mehrvarz, R. Naghipour, M. Sedghi (2006)
Colloquium Mathematicae
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Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by and are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then , the dth local cohomology module of R with respect to Φ, vanishes if and only if there...
Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)
Journal of the European Mathematical Society
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The class of loop spaces of which the mod cohomology is Noetherian is much larger than the class of -compact groups (for which the mod cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space of such an object and prove it is as small as expected, that is, comparable to that of . We also show that X differs basically from the classifying space of a -compact...
Jörg Eschmeier (2008)
Studia Mathematica
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Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.
Luc Menichi (2009)
Bulletin de la Société Mathématique de France
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Let be any compact simply-connected oriented -dimensional smooth manifold and let be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of , , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on , introduced by Chas and Sullivan. We also show that the negative cyclic...
Ursula Hamenstädt (2008)
Journal of the European Mathematical Society
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Let be an arbitrary hyperbolic geodesic metric space and let be a countable subgroup of the isometry group of . We show that if is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups , are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct...
В.М. Гольдштейн, В.И. Кузьминов, И.А. Шведов (1990)
Sibirskij matematiceskij zurnal
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Ali Atazadeh, Monireh Sedghi, Reza Naghipour (2015)
Colloquium Mathematicae
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Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration , where c = cd(,M) and denotes the largest submodule of M such that . Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module , namely . As a consequence, there exists an ideal of R such that . This generalizes the...
Michael Falk, Vadim Schechtman, Alexander Varchenko (2014)
Journal de l’École polytechnique — Mathématiques
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We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
K. Khashyarmanesh, M. Yassi, A. Abbasi (2004)
Colloquium Mathematicae
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Let R be a commutative Noetherian ring. Let and be ideals of R and let N be a finitely generated R-module. We introduce a generalization of the -finiteness dimension of relative to in the context of generalized local cohomology modules as , where M is an R-module. We also show that for any R-module M. This yields a new version of the Local-Global Principle for annihilation of local cohomology modules. Moreover, we obtain a generalization of the Faltings Lemma.
A. L. Agore (2010)
Colloquium Mathematicae
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We prove new necessary and sufficient conditions for a morphism of coalgebras to be a monomorphism, different from the ones already available in the literature. More precisely, φ: C → D is a monomorphism of coalgebras if and only if the first cohomology groups of the coalgebras C and D coincide if and only if for all . In particular, necessary and sufficient conditions for a Hopf algebra map to be a monomorphism are given.
Prakash Belkale, Swarnava Mukhopadhyay (2014)
Annales de l’institut Fourier
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We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus for classical Lie algebras and .
Edward L. Green, Nicole Snashall (2006)
Colloquium Mathematicae
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This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that , where is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements....
F. Gourdeau, Z. A. Lykova, M. C. White (2005)
Studia Mathematica
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We establish a Künneth formula for some chain complexes in the categories of Fréchet and Banach spaces. We consider a complex of Banach spaces and continuous boundary maps dₙ with closed ranges and prove that Hⁿ(’) ≅ Hₙ()’, where Hₙ()’ is the dual space of the homology group of and Hⁿ(’) is the cohomology group of the dual complex ’. A Künneth formula for chain complexes of nuclear Fréchet spaces and continuous boundary maps with closed ranges is also obtained. This enables us to describe...
Kevin P. Knudson (2002)
Fundamenta Mathematicae
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We prove that if k is a finite field with elements, then the natural map is an isomorphism for 0 ≤ i < d(p-1) and for all n.