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Algebra and Applications

Rigid Cohomology over Laurent Series Fields

Authors: Lazda, Christopher, Pal, Ambrus

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  • Presents a new cohomology theory for varieties over local function fields, taking values in the category of overconvergent (φ,∇)-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
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  • ISBN 978-3-319-30951-4
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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.

Reviews

“The book is thorough and very carefully written, with useful appendices on classical rigid cohomology, adic spaces and cohomological descent. Moreover, instead of deducing results from the known cases in classical rigid cohomology (when possible), the authors have the choice of writing down complete proofs in their setting. This makes the exposition clearer and the book self-contained. I believe that it will soon become a reference on the subject … .” (Jérôme Poineau, zbMATH 1400.14002, 2019)

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-3-319-30951-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Rigid Cohomology over Laurent Series Fields
Authors
Series Title
Algebra and Applications
Series Volume
21
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-30951-4
DOI
10.1007/978-3-319-30951-4
Hardcover ISBN
978-3-319-30950-7
Softcover ISBN
978-3-319-80926-7
Series ISSN
1572-5553
Edition Number
1
Number of Pages
X, 267
Topics