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On the Brauer class of Modular Endomorphism Algebras

Enrique González-Jiménez, Eknath Ghate, Jordi Quer

Abstract

We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the normalized slopes of the form.

On the Brauer class of Modular Endomorphism Algebras

Abstract

We investigate the Brauer class of the endomorphism algebra of the motive attached to a non-CM form. The ramification of the algebra is shown in many cases to be controlled by the normalized slopes of the form.
Paper Structure (6 sections, 9 theorems, 48 equations)

This paper contains 6 sections, 9 theorems, 48 equations.

Table of Contents

  1. Introduction
  2. Statement of results
  3. Crossed Product Structure
  4. Ramification and Slopes
  5. Bad Places
  6. Tables of QM Modular Motives

Key Result

Theorem 2.1

Let $k \geq 2$. Then $X_f$ is isomorphic to $X$.

Theorems & Definitions (17)

  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Theorem 4.1
  • proof
  • Remark 4.2
  • Theorem 4.3
  • proof
  • Remark 4.4
  • Proposition 4.5
  • ...and 7 more