Rigid cohomology

2009 ◽  
pp. 264-298
Author(s):  
Bernard Le Stum
Keyword(s):  
Rigid Cohomology

scholarly journals Rigid cohomology of topological groupoids

1978 ◽  
Vol 26 (3) ◽  
pp. 277-301 ◽  
Author(s):  
K. A. MacKenzie
Keyword(s):  
Vector Bundles ◽  
Cohomology Theory ◽  
Unexpected Result ◽  
Vertex Group ◽  
Topological Groups ◽  
Locally Compact ◽  
Cohomology Space ◽  
Rigid Cohomology ◽  
Topological Groupoids

AbstractA cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.

𝒟-modules arithmétiques sur la variété de drapeaux

2019 ◽  
Vol 2019 (754) ◽  
pp. 1-15
Author(s):  
Christine Huyghe ◽  
Tobias Schmidt
Keyword(s):  
Algebraic Group ◽  
Valuation Ring ◽  
Differential Operators ◽  
Discrete Valuation Ring ◽  
Flag Variety ◽  
Nous Obtenons ◽  
Localization Theorem ◽  
Reductive Algebraic Group ◽  
Rigid Cohomology ◽  
Complete Discrete Valuation Ring

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.

scholarly journals Product formula for p -adic epsilon factors

2014 ◽  
Vol 14 (2) ◽  
pp. 275-377 ◽  
Author(s):  
Tomoyuki Abe ◽  
Adriano Marmora
Keyword(s):  
Finite Field ◽  
Stationary Phase ◽  
Product Formula ◽  
Formula One ◽  
Etale Cohomology ◽  
Rigid Cohomology ◽  
Étale Cohomology ◽  
Analogous Formula ◽  
Epsilon Factors

AbstractLet $X$ be a smooth proper curve over a finite field of characteristic $p$. We prove a product formula for $p$-adic epsilon factors of arithmetic $\mathscr{D}$-modules on $X$. In particular we deduce the analogous formula for overconvergent $F$-isocrystals, which was conjectured previously. The $p$-adic product formula is a counterpart in rigid cohomology of the Deligne–Laumon formula for epsilon factors in $\ell$-adic étale cohomology (for $\ell \neq p$). One of the main tools in the proof of this $p$-adic formula is a theorem of regular stationary phase for arithmetic $\mathscr{D}$-modules that we prove by microlocal techniques.

scholarly journals Rigid cohomology via the tilting equivalence

2019 ◽  
Vol 223 (2) ◽  
pp. 818-843 ◽  
Author(s):  
Alberto Vezzani
Keyword(s):  
Rigid Cohomology

scholarly journals On the rigid cohomology of certain Shimura varieties

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Michael Harris ◽  
Kai-Wen Lan ◽  
Richard Taylor ◽  
Jack Thorne
Keyword(s):  
Shimura Varieties ◽  
Rigid Cohomology

ZETA-FUNCTIONS OF CERTAIN K3-FIBERED CALABI–YAU THREEFOLDS

2011 ◽  
Vol 22 (01) ◽  
pp. 67-129 ◽  
Author(s):  
YASUHIRO GOTO ◽  
REMKE KLOOSTERMAN ◽  
NORIKO YUI
Keyword(s):  
Zeta Functions ◽  
Projective Spaces ◽  
Cohomology Theory ◽  
Arithmetic Properties ◽  
Rigid Cohomology ◽  
Twist Maps

We consider certain K3-fibered Calabi–Yau threefolds. One class of such Calabi–Yau threefolds is constructed by Hunt and Schimmrigk using twist maps. They are realized in weighted projective spaces as orbifolds of hypersurfaces. Our main goal of this paper is to investigate arithmetic properties of these K3-fibered Calabi–Yau threefolds. In particular, we give detailed discussions on the construction of these Calabi–Yau varieties, singularities and their resolutions. We then determine the zeta-functions of these Calabi–Yau varieties. Next we consider deformations of our K3-fibered Calabi–Yau threefolds, and we study the variation of the zeta-functions using p-adic rigid cohomology theory.

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