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Counting abelian varieties over finite fields via Frobenius densities
Let be a principally polarized abelian variety over a finite
field with commutative endomorphism ring; further suppose that either is
ordinary or the field is prime. Motivated by an equidistribution heuristic, we
introduce a factor for each place of , and
show that the product of these factors essentially computes the size of the
isogeny class of .
The derivation of this mass formula depends on a formula of Kottwitz and on
analysis of measures on the group of symplectic similitudes, and in particular
does not rely on a calculation of class numbers.Comment: Main text by Achter, Altug and Gordon; appendix by Li and Ru
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