Rigid cohomology
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General Introduction
Rigid cohomology usually refers to the p-adic 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.
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Search results
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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??)
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Paper References
Book by Le Stum?
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Petrequin on Chern classes and cycle classes
Kedlaya on finiteness (long review)
arXiv:1205.4702 Rigid Cohomology and de Rham-Witt 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 Rham-Witt complexes with coefficients. This result generalizes the classical comparison theorem of Bloch-Illusie for proper and smooth schemes. In the proof, the key step is an extension of the Bloch-Illusie 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 Rham-Witt complex on a smooth scheme X over a perfect field K whose hypercohomology is the rigid cohomology of X in the sense of Berthelot.
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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 Rham-Witt complex by imposing a growth condition on the de Rham-Witt complex of Deligne-Illusie 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 Monsky-Washnitzer cohomology (considered before inverting p) of a smooth k-algebra is of finite type modulo torsion. This is joint work with Thomas Zink.
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