Rigid cohomology and invariant cycles for a semistable log scheme

1999 ◽  
Vol 97 (1) ◽  
pp. 155-169 ◽  
Author(s):  
Bruno Chiarellotto
Keyword(s):  
Rigid Cohomology ◽  
Log Scheme

KUMMER COVERINGS AND SPECIALISATION

2021 ◽  
pp. 1-37
Author(s):  
Martin Olsson
Keyword(s):  
Local Ring ◽  
Fundamental Groups ◽  
Technical Result ◽  
Noetherian Local Ring ◽  
Log Schemes ◽  
Log Scheme

Abstract We prove versions of various classical results on specialisation of fundamental groups in the context of log schemes in the sense of Fontaine and Illusie, generalising earlier results of Hoshi, Lepage and Orgogozo. The key technical result relates the category of finite Kummer étale covers of an fs log scheme over a complete Noetherian local ring to the Kummer étale coverings of its reduction.

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 Logarithmically regular morphisms

2020 ◽  
Author(s):  
Sam Molcho ◽  
Michael Temkin
Keyword(s):  
Simple Criterion ◽  
Log Schemes ◽  
Log Scheme

AbstractWe consider the stack $${\mathcal {L}}og_{X}$$ L o g X parametrizing log schemes over a log scheme X, and weak and strong properties of log morphisms via $${\mathcal {L}}og_{X}$$ L o g X , as defined by Olsson. We give a concrete combinatorial presentation of $${\mathcal {L}}og_{X}$$ L o g X , and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato’s chart criterion of logarithmic smoothness.

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
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