Parabolic Hecke Eigensheaves / Ron Donagi & Tony Pantev.

Format:

Book

Author/Creator:

Donagi, Ron, author.

Pantev, Tony, 1963- author.

Series:

Astérisque ; 435.

Astérisque, 0303-1179 ; 435

Language:

English

French

Subjects (All):

Hodge theory.

Hecke algebras.

Parabolic operators.

Physical Description:

viii, 192 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, [2022]

Language Note:

Abstract also in French.

Summary:

We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line C with tame ramification at five points {p1,p2,p3,p4,p5}. In particular we construct the automorphic D-modules predicted by GLC on the moduli space of rank two parabolic bundles on (C,{p1,p2,p3,p4,p5}). The construction uses non-abelian Hodge theory and a Fourier-Mukai transform along the fibers of the Hitchin fibration to reduce the problem to one in classical projective geometry on the intersection of two quadrics in P4.

Contents:

Introduction

Parabolic objects

Moduli spaces

The Hecke correspondence

The modular spectral cover

Hecke Eigensheaves

Solving the constraints

Summary.

Notes:

Includes bibliographical references (pages 181-186) and index.

Current Copyright Fee: GBP22.50 0.

ISBN:

9782856299609

2856299601

OCLC:

1350632608