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An Excursion into $p$-Adic Hodge Theory: From Foundations to Recent Trends
 
Fabrizio Andreatta Universita degli Studi di Milano, Milano, Italy
Riccardo Brasca Institut de Mathématiques de Jussieu, Université Paris Diderot, Paris, France
Olivier Brinon Université de Bordeaux, Talence, France
Xavier Caruso Université de Bourdeaux, Talence, France
Bruno Chiarellotto University of Padova, Italy
Gerard Freixas i Montplet Institut de Mathématiques de Jussieu, Université Paris Diderot, Paris, France
Shin Hattori Tokyo City University, Tokyo, Japan
Nicola Mazzari Université de Bourdeaux, Talence, France
Simone Panozzo Universita degli Studi di Milano, Milano, Italy
Marco Seveso Universita degli Studi di Milano, Milano, Italy
Go Yamashita Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
A publication of the Société Mathématique de France
An Excursion into p-Adic Hodge Theory
Softcover ISBN:  978-2-85629-913-5
Product Code:  PASY/54
List Price: $75.00
AMS Member Price: $60.00
Please note AMS points can not be used for this product
An Excursion into p-Adic Hodge Theory
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An Excursion into $p$-Adic Hodge Theory: From Foundations to Recent Trends
Fabrizio Andreatta Universita degli Studi di Milano, Milano, Italy
Riccardo Brasca Institut de Mathématiques de Jussieu, Université Paris Diderot, Paris, France
Olivier Brinon Université de Bordeaux, Talence, France
Xavier Caruso Université de Bourdeaux, Talence, France
Bruno Chiarellotto University of Padova, Italy
Gerard Freixas i Montplet Institut de Mathématiques de Jussieu, Université Paris Diderot, Paris, France
Shin Hattori Tokyo City University, Tokyo, Japan
Nicola Mazzari Université de Bourdeaux, Talence, France
Simone Panozzo Universita degli Studi di Milano, Milano, Italy
Marco Seveso Universita degli Studi di Milano, Milano, Italy
Go Yamashita Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-913-5
Product Code:  PASY/54
List Price: $75.00
AMS Member Price: $60.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Panoramas et Synthèses
    Volume: 542020; 268 pp
    MSC: Primary 14; 11

    This volume offers a progressive and comprehensive introduction to \(p\)-adic Hodge theory. It starts with Tate's works on \(p\)-adic divisible groups and the cohomology of \(p\)-adic varieties, which constitutes the main concrete motivations for the development of \(p\)-adic Hodge theory. It then moves smoothly to the construction of Fontaine's \(p\)-adic period rings and their apparition in several comparison theorems between various \(p\)-adic cohomologies. Applications and generalizations of these theorems are subsequently discussed. Finally, Scholze's modern vision on \(p\)-adic Hodge theory, based on the theory of perfectoids, is presented.

    A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 542020; 268 pp
MSC: Primary 14; 11

This volume offers a progressive and comprehensive introduction to \(p\)-adic Hodge theory. It starts with Tate's works on \(p\)-adic divisible groups and the cohomology of \(p\)-adic varieties, which constitutes the main concrete motivations for the development of \(p\)-adic Hodge theory. It then moves smoothly to the construction of Fontaine's \(p\)-adic period rings and their apparition in several comparison theorems between various \(p\)-adic cohomologies. Applications and generalizations of these theorems are subsequently discussed. Finally, Scholze's modern vision on \(p\)-adic Hodge theory, based on the theory of perfectoids, is presented.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.