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Fields with no everywhere good abelian varieties

Armand Brumer, Kenneth Kramer

Abstract

We extend methods of Fontaine, Abrashkin and Schoof to obtain criteria determining number fields K over which no non-zero abelian variety with everywhere good reduction exists. As an application, under the GRH, we find 24744 such fields of various degrees up to 16.

Fields with no everywhere good abelian varieties

Abstract

We extend methods of Fontaine, Abrashkin and Schoof to obtain criteria determining number fields K over which no non-zero abelian variety with everywhere good reduction exists. As an application, under the GRH, we find 24744 such fields of various degrees up to 16.
Paper Structure (7 sections, 33 theorems, 58 equations, 2 tables)

This paper contains 7 sections, 33 theorems, 58 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Applications of higher ramification bounds
  3. Some group theory
  4. The relevant group schemes
  5. Some number theory
  6. About abelian varieties
  7. How were the computations done?

Key Result

Proposition 1.5

Assume the hypotheses of Proposition DpTest1.

Theorems & Definitions (63)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Proposition 1.5
  • Theorem 2.2
  • Proposition 2.3
  • proof
  • Proposition 2.7
  • proof
  • Lemma 2.8
  • ...and 53 more