Overview
- Presents a new cohomology theory for varieties over local function fields, taking values in the category of overconvergent (f,?)-modules
- Introduces coefficient objects for this newly developed cohomology theory, providing a bridge between the local and global pictures
- Proves a p-adic weight monodromy conjecture in equicharacteristic p
- Includes supplementary material: sn.pub/extras
Part of the book series: Algebra and Applications (AA, volume 21)
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Table of contents (5 chapters)
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About this book
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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Bibliographic Information
Book Title: Rigid Cohomology over Laurent Series Fields
Authors: Christopher Lazda, Ambrus Pál
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-3-319-30951-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-30950-7Published: 09 May 2016
Softcover ISBN: 978-3-319-80926-7Published: 27 May 2018
eBook ISBN: 978-3-319-30951-4Published: 27 April 2016
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: X, 267
Topics: Algebraic Geometry, Number Theory