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

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.

15 pages. Final version