1. Super-isolated abelian varieties.
- Author
-
Scholl, Travis
- Subjects
- *
ABELIAN varieties , *ALGEBRAIC number theory , *FINITE fields , *ELLIPTIC curve cryptography , *ALGEBRAIC varieties - Abstract
We call an abelian variety over a finite field F q super-isolated if its (F q -rational) isogeny class contains a single isomorphism class. In this paper, we use the Honda-Tate theorem to characterize super-isolated ordinary simple abelian varieties by certain algebraic integers. Our main result is that for a fixed dimension g ≥ 3 , there are finitely many such varieties over all finite fields. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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