• Corpus ID: 43801434

# Rigid cohomology over Laurent series field I: First definitions and basic properties

@article{Lazda2014RigidCO,
title={Rigid cohomology over Laurent series field I: First definitions and basic properties},
author={Christopher Lazda and Ambrus P'al},
journal={arXiv: Number Theory},
year={2014}
}
• Published 25 November 2014
• Mathematics
• arXiv: Number Theory
This is the first in a series of papers in which we construct and study a new $p$-adic cohomology theory for varieties over Laurent series fields $k(\!(t)\!)$ in characteristic $p$. This will be a version of rigid cohomology, taking values in the bounded Robba ring $\mathcal{E}_K^\dagger$, and in this paper, we give the basic definitions and constructions. The cohomology theory we define can be viewed as a relative version of Berthelot's rigid cohomology, and is constructed by compactifying $k… ## References SHOWING 1-10 OF 14 REFERENCES A generalization of formal schemes and rigid analytic varieties In this paper we construct a natural category ~r of locally and topologically ringed spaces which contains both the category of locally noetherian formal schemes and the category of rigid analytic Finiteness of rigid cohomology with coefficients We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology The de Rham-Witt complex and p-adic vanishing cycles • Mathematics • 2003 We determine the structure modulo p of the de Rham-Witt complex of a smooth scheme X over a discrete valuation ring of mixed characteristic with log-poles along the special fiber Y and show that the Syntomic complexes and p-adic vanishing cycles. Let A be a complete discrete valuation ring with field of fractions K of characteristic 0 and with perfect residue field k of characteristic p > 0, and let W be the ring of Wittvectors with Facteurs epsilon p-adiques Abstract We develop and study the epsilon factor of a ‘local system’ of p-adic coefficients over the spectrum of a complete discrete valuation field K with finite residue field of characteristic p>0. Étale Cohomology of Rigid Analytic Varieties and Adic Spaces Summary of the results on the etale cohomology of rigid analytic varieties - Adic spaces - The etale site of a rigid analytic variety and an adic space - Comparison theorems - Base change theorems - Rigid analytic geometry and its applications • Mathematics • 2003 Preface.- Valued fields and normed spaces.- The projective line.- Affinoid algebras.- Rigid spaces.- Curves and their reductions.- Abelian varieties.- Points of rigid spaces, rigid cohomology.- Etale Spectral Theory and Analytic Geometry over Non-Archimedean Fields The spectrum of a commutative Banach ring Affinoid spaces Analytic spaces Analytic curves Analytic groups and buildings The homotopy type of certain analytic spaces Spectral theory Perturbation Géométrie rigide et cohomologie des variétés algébriques de caractéristique$p\$
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Foundations of rigid geometry I, preprint (2013), arXiv:math/1308.4734v1, to appear in Monographs in Mathematics
• 2013