Rigid Cohomology over Laurent Series Fields

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Rigid Cohomology over Laurent Series Fields by Christopher Lazda, Ambrus Pál, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Christopher Lazda, Ambrus Pál ISBN: 9783319309514
Publisher: Springer International Publishing Publication: April 27, 2016
Imprint: Springer Language: English
Author: Christopher Lazda, Ambrus Pál
ISBN: 9783319309514
Publisher: Springer International Publishing
Publication: April 27, 2016
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book The Road to Discovery by Christopher Lazda, Ambrus Pál
Cover of the book Agro-Environmental Sustainability by Christopher Lazda, Ambrus Pál
Cover of the book New Perspectives in End-User Development by Christopher Lazda, Ambrus Pál
Cover of the book PET/CT in Lung Cancer by Christopher Lazda, Ambrus Pál
Cover of the book Surviving Dementia by Christopher Lazda, Ambrus Pál
Cover of the book One Hundred Prisoners and a Light Bulb by Christopher Lazda, Ambrus Pál
Cover of the book Modern Marriage and the Lyric Sequence by Christopher Lazda, Ambrus Pál
Cover of the book New Directions in Spiritual Kinship by Christopher Lazda, Ambrus Pál
Cover of the book James Bond Uncovered by Christopher Lazda, Ambrus Pál
Cover of the book The Auditory System at the Cocktail Party by Christopher Lazda, Ambrus Pál
Cover of the book Financial Accounting and Management Control by Christopher Lazda, Ambrus Pál
Cover of the book HCI in Business, Government, and Organizations: Information Systems by Christopher Lazda, Ambrus Pál
Cover of the book NASA Formal Methods by Christopher Lazda, Ambrus Pál
Cover of the book Bullying and Violence in South Korea by Christopher Lazda, Ambrus Pál
Cover of the book History, Philosophy and Science Teaching by Christopher Lazda, Ambrus Pál
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy