Achter, Jeffrey D;
Altuğ, S Ali;
Garcia, Luis;
Gordon, Julia;
Li, Wen-Wei;
Rüd, Thomas;
(2023)
Counting abelian varieties over finite fields via Frobenius densities.
Algebra & Number Theory
, 17
(7)
pp. 1239-1280.
10.2140/ant.2023.17.1239.
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Abstract
Let [X, λ] be a principally polarized abelian variety over a finite field with commutative endomorphism ring; further suppose that either X is ordinary or the field is prime. Motivated by an equidistribution heuristic, we introduce a factor νv([X, λ]) for each place v of Q, and show that the product of these factors essentially computes the size of the isogeny class of [X, λ]. 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.
| Type: | Article |
|---|---|
| Title: | Counting abelian varieties over finite fields via Frobenius densities |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/ant.2023.17.1239 |
| Publisher version: | https://doi.org/10.2140/ant.2023.17.1239 |
| Language: | English |
| Additional information: | Copyright © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY), https://creativecommons.org/licenses/by/4.0/. Open Access made possible by subscribing institutions via Subscribe to Open. |
| Keywords: | Abelian variety, isogeny class, orbital integral |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10183003 |
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