• Corpus ID: 36565448

# Rigid cohomology over Laurent series fields II: Finiteness and Poincar\'e duality for smooth curves

@article{Lazda2014RigidCO,
title={Rigid cohomology over Laurent series fields II: Finiteness and Poincar\'e duality for smooth curves},
author={Christopher Lazda and Ambrus P'al},
journal={arXiv: Number Theory},
year={2014}
}
• Published 17 December 2014
• Mathematics
• arXiv: Number Theory
In this paper we prove that the $\mathcal{E}^\dagger_K$-valued cohomology, introduced in [9] is finite dimensional for smooth curves over Laurent series fields $k((t))$ in positive characteristic, and forms an $\mathcal{E}^\dagger_K$-lattice inside `classical' $\mathcal{E}_K$-valued rigid cohomology. We do so by proving a suitable version of the p-adic local monodromy theory over $\mathcal{E}^\dagger_K$, and then using an \'{e}tale pushforward for smooth curves to reduce to the case of $\mathbb… ## References SHOWING 1-10 OF 10 REFERENCES Rigid cohomology over Laurent series fields III: Absolute coefficients and arithmetic applications • Mathematics • 2015 In this paper we investigate the arithmetic aspects of the theory of$\mathcal{E}_K^\dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology Rigid Cohomology over Laurent Series Fields • Mathematics • 2016 In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many Finiteness of rigid cohomology with coefficients We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve Abstract Let M be an overconvergent isocrystal on a smooth affine curve X / k over a perfect field of characteristic p > 0, realized as a module on a suitable lifting of X with connection. We give a A p-adic local monodromy theorem We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential More étale covers of affine spaces in positive characteristic We prove that every geometrically reduced projective variety of pure dimension n over a field of positive characteristic admits a morphism to projective n-space, etale away from the hyperplane H at Lectures on Formal and Rigid Geometry Classical Rigid Geometry.- Tate Algebras.- Affinoid Algebras and their Associated Spaces.- Affinoid Functions.- Towards the Notion of Rigid Spaces.- Coherent Sheaves on Rigid Spaces.- Formal Géométrie rigide et cohomologie des variétés algébriques de caractéristique$p\$
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