Fully maximal and fully minimal abelian varieties

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 varietie...

Full description

Saved in:
Bibliographic Details
Published inJournal of pure and applied algebra Vol. 223; no. 7; pp. 3031 - 3056
Main Authors Karemaker, Valentijn, Pries, Rachel
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2019
Subjects
Abelian variety
Curve
Maximal
Supersingular
Weil number
Zeta function
secondary
Maximal
Primary
Curve
Zeta function
Abelian variety
Supersingular
Weil number
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.10.007