The p-adic Simpson Correspondence (AM-193)

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book The p-adic Simpson Correspondence (AM-193) by Ahmed Abbes, Michel Gros, Takeshi Tsuji, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Ahmed Abbes, Michel Gros, Takeshi Tsuji ISBN: 9781400881239
Publisher: Princeton University Press Publication: February 9, 2016
Imprint: Princeton University Press Language: English
Author: Ahmed Abbes, Michel Gros, Takeshi Tsuji
ISBN: 9781400881239
Publisher: Princeton University Press
Publication: February 9, 2016
Imprint: Princeton University Press
Language: English

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.

The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.

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

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation.

The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.

More books from Princeton University Press

Cover of the book Think Again by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Validated Numerics by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book The Godfather Doctrine by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Accelerating Democracy by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Financial Crisis, Contagion, and Containment by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Strategic Reassurance and Resolve by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Art of the Deal by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics (New in Paperback) by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book The Propriety of Liberty by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book The Five Habits of Highly Effective Honeybees (and What We Can Learn from Them) by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book The Democracy Index by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Einstein and Religion by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book The Origins of the Urban Crisis by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Visions of Empire by Ahmed Abbes, Michel Gros, Takeshi Tsuji
Cover of the book Dry Bones Rattling by Ahmed Abbes, Michel Gros, Takeshi Tsuji
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