Rigid Cohomology over Laurent Series Fields
Springer International Publishing (Verlag)
978-3-319-30950-7 (ISBN)
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.
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
"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)
“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)
| Erscheinungsdatum | 03.05.2016 |
|---|---|
| Reihe/Serie | Algebra and Applications |
| Zusatzinfo | X, 267 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Algebraic Geometry • local function fields • mathematics and statistics • Number Theory • p-adic cohomology • (phi, )-modules • (phi,)-modules • rigid geometry • weight-monodromy • (φ,∇)-modules |
| ISBN-10 | 3-319-30950-1 / 3319309501 |
| ISBN-13 | 978-3-319-30950-7 / 9783319309507 |
| Zustand | Neuware |
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