Fully maximal and fully minimal abelian varieties

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Karemaker, Valentijn¹  Pries, Rachel² 

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[2] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

关键词: Abelian variety;    Curve;    Supersingular;    Maximal;    Zeta function;    Weil number;   

DOI  :  10.1016/j.jpaa.2018.10.007

来源: Elsevier

【 摘 要 】

We introduce and study a new way to categorize supersingular abelian varieties defined over a finite field by classifying them as fully maximal, mixed or fully minimal. The type of A depends on the normalized Weil numbers of A and its twists. We analyze these types for supersingular abelian varieties and curves under conditions on the automorphism group. In particular, we present a complete analysis of these properties for supersingular elliptic curves and supersingular abelian surfaces in arbitrary characteristic, and for a one-dimensional family of supersingular curves of genus 3 in characteristic 2. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free