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##
Faltings Heights and *L*-functions: Minicourse Given by Shou-Wu Zhang

*Ziyang Gao, Rafael von Känel, and Lucia Mocz*

### 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/9780691193779.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter explores Shou-Wu Zhang's minicourse on Faltings heights and L-functions. It essentially consists of three parts. The first part discusses conjectures and results in the literature which ... More

## Open Quantum Electrodynamics

*Heinz-Peter Breuer and Francesco Petruccione*

### in The Theory of Open Quantum Systems

- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199213900
- eISBN:
- 9780191706349
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213900.003.12
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In quantum electrodynamics, the matter degrees of freedom are coupled to the radiation field through a local, gauge-invariant interaction density. Due to the linear structure of this coupling, the ... More

## Introduction

*Dennis Gaitsgory and Jacob Lurie*

### in Weil's Conjecture for Function Fields: Volume I (AMS-199)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691182148
- eISBN:
- 9780691184432
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691182148.003.0001
- Subject:
- Mathematics, Mathematical Finance

This introductory chapter sets out the book's purpose, which is to study Weil's conjecture over function fields: that is, fields K which arise as rational functions on an algebraic curve X over a ... More

## Random matrices and number theory: some recent themes

*Jon P. Keating*

### in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198797319
- eISBN:
- 9780191838774
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198797319.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and ... More

## Interacting Electron–Hole–Phonon System

*Norman J. Morgenstern Horing*

### in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 11 employs variational differential techniques and the Schwinger Action Principle to derive coupled-field Green’s function equations for a multi-component system, modeled as an interacting ... More

## Graphene

*Norman J. Morgenstern Horing*

### in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198791942
- eISBN:
- 9780191834165
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198791942.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac ... 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

##
The Formalism of *l*-adic Sheaves

*Dennis Gaitsgory and Jacob Lurie*

### in Weil's Conjecture for Function Fields: Volume I (AMS-199)

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780691182148
- eISBN:
- 9780691184432
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691182148.003.0002
- Subject:
- Mathematics, Mathematical Finance

The ℓ-adic product formula discussed in Chapter 4 will need to make use of analogous structures, which are simply not visible at the level of the triangulated category Dℓ(X). This chapter attempts to ... More

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