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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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