Size of isogeny classes of abelian varieties of Lubin-Tate type

TL;DR

This paper establishes a lower bound for the size of isogeny classes of certain abelian varieties over finite fields and conjectures its sharpness based on Newton stratum expectations.

Contribution

It provides a new lower bound for isogeny class sizes of simple abelian varieties of Lubin-Tate type over finite fields.

Findings

Proved a lower bound for isogeny class size.

Conjectured the bound's sharpness based on Newton stratum analysis.

Highlights the relationship between endomorphism rings and isogeny class sizes.

Abstract

We prove a lower bound for the size of the isogeny class of a simple abelian variety over a finite field with commutative endomorphism ring in the Lubin-Tate case. Moreover, based on the expected size of the isogeny classes in the Newton stratum, we conjecture that this lower bound is sharp.