-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...
Sonia L’Innocente, Françoise Point, Carlo Toffalori (2013)
Confluentes Mathematici
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We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra . We discuss two cases, according to whether the parameter is a root of unity. We show that the universal enveloping algebra of embeds in a non-principal ultraproduct of , where varies over the primitive roots of unity.
Tomáš Rusin (2019)
Archivum Mathematicum
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We use known results on the characteristic rank of the canonical –plane bundle over the oriented Grassmann manifold to compute the generators of the –cohomology groups for . Drawing from the similarities of these examples with the general description of the cohomology rings of we conjecture some predictions.
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.
Lawrence C. Evans (2000-2001)
Séminaire Équations aux dérivées partielles
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We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function solving the eikonal equation aėȧnd a probability measure solving a related transport equation. We present some elementary formal identities relating certain quantum states and . We show also how...
Jialei Chen, Shilin Yang (2022)
Czechoslovak Mathematical Journal
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We first describe the Sekine quantum groups (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of and describe their representation rings . Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of .
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...
Shahram Rezaei (2019)
Commentationes Mathematicae Universitatis Carolinae
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Let be an ideal of Noetherian local ring and a finitely generated -module of dimension . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to . Also we prove that for an arbitrary local ring (not necessarily complete), we have
Gilles Pisier (2014)
Journal of the European Mathematical Society
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We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the “growth" of certain operator spaces: It implies asymptotically sharp estimates for the growth of the multiplicity of -spaces needed to represent (up to a constant ) the -version of the -dimensional operator Hilbert space as a direct sum of copies of . We show that, when is close to 1, this multiplicity grows...
Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau, Huaiqing Zuo (2014)
Journal of the European Mathematical Society
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It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function which is the number of positive integers and free of prime factors . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional () real right-angled simplices. In this...
Seyed Ebrahim Akrami, Shervin Farzi (2020)
Mathematica Bohemica
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We introduce a method for construction of a covariant differential calculus over a Hopf algebra from a quantized calculus , , where is a candidate for a Dirac operator for . We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra . We apply this method to the Dirac operator for the quantum given by S. Majid. We find that the differential calculus obtained by our...
Zhenzhen Feng, Xiaosong Sun (2019)
Czechoslovak Mathematical Journal
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We show that the GVC (generalized vanishing conjecture) holds for the differential operator and all polynomials , where is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.
Janusz Wysoczański (2010)
Banach Center Publications
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We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators on with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra associated with the quantum group . The purpose of this note is to present the construction.
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...
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...
Xia Xu, Yong Yang (2023)
Czechoslovak Mathematical Journal
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We improve a few results related to Huppert’s - conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.