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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


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


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


Shtukas with one leg II

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/9780691202082.003.0013
Subject:
Mathematics, Geometry / Topology

This chapter offers a second lecture on one-legged shtukas. It shows that a shtuka over Spa Cb, a priori defined over Y[0,INFINITY) = Spa Ainf REVERSE SOLIDUS {xk, xL}, actually extends to Y = Spa ... More


Introduction

Peter Scholze and Jared Weinstein

in Berkeley Lectures on p-adic Geometry

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of Drinfeld's work on the global Langlands correspondence over function fields. Whereas the global Langlands correspondence is largely open in the case ... More


Shtukas with one leg III

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/9780691202082.003.0014
Subject:
Mathematics, Geometry / Topology

This chapter presents a third lecture on one-legged shtukas. The goal is to complete the proof of Fargues' theorem. To complete the proof of Fargues' theorem, it remains to prove the following ... More


Vector bundles and G-torsors on the relative Fargues-Fontaine curve

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/9780691202082.003.0022
Subject:
Mathematics, Geometry / Topology

This chapter discusses vector bundles and G-torsors on the relative Fargues-Fontaine curve. This is in preparation for the examination of moduli spaces of shtukas. Kedlaya-Liu prove two important ... More


Moduli spaces of 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/9780691202082.003.0023
Subject:
Mathematics, Geometry / Topology

This chapter examines the moduli spaces of mixed-characteristic local G-shtukas and shows that they are representable by locally spatial diamonds. These will be the mixed-characteristic local ... More


Local Shimura varieties

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/9780691202082.003.0024
Subject:
Mathematics, Geometry / Topology

This chapter specializes the theory back to the case of local Shimura varieties, and explains the relation with Rapoport-Zink spaces. It begins with a local Shimura datum. A local Shimura datum is a ... More


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