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The p-adic Simpson Correspondence (AM-193)

Ahmed Abbes, Michel Gros, and Takeshi Tsuji

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170282
eISBN:
9781400881239
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170282.001.0001
Subject:
Mathematics, Algebra

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 ... More


Facsimile : A p-adic Simpson correspondence

Gerd Faltings

in The p-adic Simpson Correspondence (AM-193)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170282
eISBN:
9781400881239
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170282.003.0007
Subject:
Mathematics, Algebra

This chapter presents the facsimile of Gerd Faltings' article entitled “A p-adic Simpson Correspondence,” reprinted from Advances in Mathematics 198(2), 2005. In this article, an equivalence between ... More


Berkeley Lectures on p-adic Geometry: (AMS-207)

Peter Scholze and Jared Weinstein

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents an important breakthrough in arithmetic geometry. In 2014, this book's author delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory ... More


Covanishing topos and generalizations

Ahmed Abbes, Michel Gros, and Takeshi Tsuji

in The p-adic Simpson Correspondence (AM-193)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170282
eISBN:
9781400881239
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170282.003.0006
Subject:
Mathematics, Algebra

This chapter focuses on the Faltings topos, the general framework for Faltings' approach in p-adic Hodge theory. It presents a new approach to the Faltings topos based on a generalization of ... More


Shtukas with one leg

Peter Scholze and Jared Weinstein

in Berkeley Lectures on p-adic Geometry: (AMS-207)

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter analyzes shtukas with one leg over a geometric point in detail, and discusses the relation to (integral) p-adic Hodge theory. It focuses on the connection between shtukas with one leg ... More


Mixed-characteristic shtukas

Peter Scholze and Jared Weinstein

in Berkeley Lectures on p-adic Geometry: (AMS-207)

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter looks at mixed-characteristic shtukas. Much of the theory of mixed-characteristic shtukas is motivated by the structures appearing in (integral) p-adic Hodge theory. The chapter assesses ... More


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