Counting abelian varieties over finite fields via Frobenius densities
| Autor: | Achter, Jeff, Altug, Salim Ali, Garcia, Luis, Gordon, Julia, Li, Wen-Wei, Rüd, Thomas |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 17 (2023) 1239-1280 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2023.17.1239 |
| Popis: | Let $[X,\lambda]$ 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 $\nu_v([X,\lambda])$ for each place $v$ of $\mathbb Q$, and show that the product of these factors essentially computes the size of the isogeny class of $[X,\lambda]$. 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: Added author; significantly simplified global calculation in section 5; made other, smaller improvements |
| Databáze: | arXiv |
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