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Rigid cohomology over Laurent series fields

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Rigid cohomology over Laurent series fields/ by Christopher Lazda, Ambrus Pal.
Author:	Lazda, Christopher.
other author:	Pal, Ambrus.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	x, 267 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Cohomology operations. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-30951-4
ISBN:	9783319309514

Rigid cohomology over Laurent series fields
Lazda, Christopher.

Rigid cohomology over Laurent series fields[electronic resource] /by Christopher Lazda, Ambrus Pal. - Cham :Springer International Publishing :2016. - x, 267 p. :ill., digital ;24 cm. - Algebra and applications,v.211572-5553 ;. - Algebra and applications ;v.17..

Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.

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 major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.

ISBN: 9783319309514

Standard No.: 10.1007/978-3-319-30951-4doiSubjects--Topical Terms:

898172
Cohomology operations.

LC Class. No.: QA169

Dewey Class. No.: 514.23

Rigid cohomology over Laurent series fields
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505 0 $a Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.
520 $a 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 major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.
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