Rigid cohomology over Laurent series fields / by Christopher Lazda, Ambrus Pál.

Format:

Book

Author/Creator:

Lazda, Christopher, Author.

Pál, Ambrus, Author.

Series:

Algebra and Applications, 1572-5553 ; 21

Language:

English

Subjects (All):

Geometry, Algebraic.

Number theory.

Algebraic Geometry.

Number Theory.

Local Subjects:

Algebraic Geometry.

Number Theory.

Physical Description:

1 online resource (271 p.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

3-319-30951-X