Rigid cohomology

General Introduction
Rigid cohomology usually refers to the padic cohomology theory described for example in the book of Le Stum, but there is a paper by Voevodsky (Open problems...) in which he uses the terms rigid homotopy and rigid homology for something completely different.
<]]> 
Search results
<]]> 
Online References
Something might be here
Some questions of Kedlaya
Berthelot, P.: Cohomologie rigide et cohomologie rigide `a supports propres. Pr´epublication (1996) (is this online??)
<]]> 
Paper References
Book by Le Stum?
<]]> 
Definition
<]]> 
Properties
<]]> 
Standard theorems
<]]> 
Open Problems
<]]> 
Connections to Number Theory
<]]> 
Computations and Examples
<]]> 
History and Applications
<]]> 
Some Research Articles
Petrequin on Chern classes and cycle classes
Kedlaya on finiteness (long review)
arXiv:1205.4702 Rigid Cohomology and de RhamWitt complexes from arXiv Front: math.AG by Pierre Berthelot Let $k$ be a perfect field of characteristic $p > 0$, $Wn = Wn(k)$. For separated $k$schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de RhamWitt complexes with coefficients. This result generalizes the classical comparison theorem of BlochIllusie for proper and smooth schemes. In the proof, the key step is an extension of the BlochIllusie theorem to the case of cohomologies relative to $Wn$ with coefficients in a crystal that is only supposed to be flat over $Wn$.
arXiv:1008.0305 Overconvergent Witt Vectors from arXiv Front: math.AG by Christopher Davis, Andreas Langer, Thomas Zink Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vectors. We prove that on a scheme X of finite type over K the overconvergent Witt vectors are an étale sheaf. In a forthcoming paper (Annales ENS) we define an overconvergent de RhamWitt complex on a smooth scheme X over a perfect field K whose hypercohomology is the rigid cohomology of X in the sense of Berthelot.
<]]> 
Other Information
Andreas Langer (Exeter) "An integral structure on rigid cohomology" (MR13, 2:30pm as usual)
Abstract: For a quasiprojective smooth variety over a perfect field k of char p we introduce an overconvergent de RhamWitt complex by imposing a growth condition on the de RhamWitt complex of DeligneIllusie using Gauus norms and prove that its hypercohomology defines an integral structure on rigid cohomology, i.e. its image in rigid cohomology is a canonical lattice. As a corollary we obtain that the integral MonskyWashnitzer cohomology (considered before inverting p) of a smooth kalgebra is of finite type modulo torsion. This is joint work with Thomas Zink.
<]]> 
Comments Posted
<]]> 
Comments
There are no comments.