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Local Shimura Varieties: Minicourse Given by Peter Scholze

Gisbert Wüstholz and Clemens Fuchs (eds)

in Arithmetic and Geometry: Ten Years in Alpbach

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter discusses Peter Scholze's minicourse on local Shimura varieties. The goal of these lectures is to describe a program to construct local Langlands correspondence. The construction is ... More


GEOMETRIC MODULAR FORMS

Haruzo Hida

in Hilbert Modular Forms and Iwasawa Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198571025
eISBN:
9780191718946
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571025.003.0004
Subject:
Mathematics, Algebra

This chapter discusses p-adic automorphic forms on Shimura variety from Springer, recalling the exact control theorem which connects the specialization (at a given weight) of the universal nearly ... More


Shimura Varieties: A Hodge-Theoretic Perspective

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)

in Hodge Theory (MN-49)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter discusses certain cleverly constructed unions of modular varieties, called Shimura varieties, in the Hodge-theoretic perspective. The Shimura varieties can show the minimal (i.e., ... More


About the André-Oort Conjecture

Umberto Zannier

in Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153704
eISBN:
9781400842711
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153704.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter discusses some aspects of the so-called André–Oort conjecture. It observes how this resembles the pattern of the statements discussed so far, recalling also a brief history. After a few ... More


Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Gisbert Wüstholz and Clemens Fuchs (eds)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.001.0001
Subject:
Mathematics, Geometry / Topology

This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the ... More


Introduction

Gisbert Wüstholz and Clemens Fuchs (eds)

in Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691193779
eISBN:
9780691197548
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691193779.003.0001
Subject:
Mathematics, Geometry / Topology

This introductory chapter provides an overview of the three topics discussed in this book: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and ... More


Hodge Theory (MN-49)

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161341
eISBN:
9781400851478
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161341.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The ... More


Integral models of 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/9780691202082.003.0025
Subject:
Mathematics, Geometry / Topology

This chapter explains an application of the theory developed in these lectures towards the problem of understanding integral models of local Shimura varieties. As a specific example, it resolves ... 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


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


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