Rigid Cohomology over Laurent Series Fields: Algebra and Applications, cartea 21
Autor Christopher Lazda, Ambrus Pálen Limba Engleză Hardback – 9 mai 2016
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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Specificații
ISBN-13: 9783319309507
ISBN-10: 3319309501
Pagini: 267
Ilustrații: X, 267 p.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.57 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Algebra and Applications
Locul publicării:Cham, Switzerland
ISBN-10: 3319309501
Pagini: 267
Ilustrații: X, 267 p.
Dimensiuni: 155 x 235 x 18 mm
Greutate: 0.57 kg
Ediția:1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Algebra and Applications
Locul publicării:Cham, Switzerland
Cuprins
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
Recenzii
“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)
Textul de pe ultima copertă
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.
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.
Caracteristici
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