Rigid Cohomology over Laurent Series Fields
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- Synopsis
- In this monograph, the authors develop a new theory of p-adiccohomology for varieties over Laurent series fields in positive characteristic,based on Berthelot's theory of rigid cohomology. Many major fundamentalproperties of these cohomology groups are proven, such as finite dimensionalityand cohomological descent, as well asinterpretations in terms of Monsky-Washnitzer cohomology and Le Stum'soverconvergent site. Applications of this new theory to arithmetic questions, such as l-independenceand the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to theGalois representations associated tovarieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theoriesover function fields. By extending the scope of existing methods, the results presented here also serve as a firststep towards a more general theory of p-adic cohomology overnon-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in thearithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adicspaces make it as self-contained as possible, and an ideal starting point forgraduate students looking to explore aspects of the classical theory of rigidcohomology and with an eye towards future research in the subject.
- Copyright:
- 2016
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783319309514
- Publisher:
- Springer International Publishing, Cham
- Date of Addition:
- 11/14/16
- Copyrighted By:
- Springer
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.