Holmstrom Rigid cohomology

Rigid cohomology

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Rigid cohomology

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Rigid cohomology

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Rigid cohomology

Book by Le Stum?

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Rigid cohomology

Something might be here

Some questions of Kedlaya

Berthelot, P.: Cohomologie rigide et cohomologie rigide `a supports propres. Pr´epublication (1996) (is this online??)


Rigid cohomology

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.


Rigid cohomology

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.


Rigid cohomology

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 kk be a perfect field of characteristic p>0p > 0, W n=W n(k)W_n = W_n(k). For separated kk-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 W nW_n with coefficients in a crystal that is only supposed to be flat over W nW_n.

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.

nLab page on Rigid cohomology

Created on June 10, 2014 at 21:14:54 by Andreas Holmström