Conjectures and results on modular representations of GLn (K) for a p-Adic field K / by Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, and Benjamin Schraen.

Format:

Book

Author/Creator:

Breuil, Christophe, 1968- author.

Herzig, Florian, author.

Hu, Yongquan, author.

Morra, Stefano, author.

Schraen, Benjamin, author.

Series:

Memoirs of the American Mathematical Society ; volume 315, no. 1598.

Memoirs of the American Mathematical Society, 0065-9266 ; volume 315, no. 1598

Language:

English

Subjects (All):

Prediction (Logic).

Iwasawa theory.

Physical Description:

v, 163 pages : illustrations, 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2025.

Summary:

Let p be a prime number and K a finite extension of Qp. We state conjectures on the smooth representations of GLn(K) that occur in spaces of mod p automorphic forms (for compact unitary groups). In particular, when K is unramified, we conjecture that they are of finite length and predict their internal structure (extensions, form of subquotients) from the structure of a certain algebraic representation of GLn. When n=2 and K is unramified, we prove several cases of our conjectures, including new finite length results.

Contents:

1. Introduction

2. Local-global compatibility conjectures

3. The case of GL_2(Qpf)

Notes:

Number 1598 (second of 6 numbers)

Includes bibliographical references.

'Number 1598 (second of 6 numbers)' -- Cover.

ISBN:

1470478366

9781470478360

OCLC:

1560085086