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arXiv · 1403.3037

Local heuristics and an exact formula for abelian surfaces over finite fields

Jeff Achter·Cassie Williams
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Abstract

Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistribution considerations we define, for each prime $\ell$, a local factor which measures the relative frequency with which $f\bmod \ell$ occurs as the characteristic polynomial of a symplectic similitude over $\mathbb{F}_\ell$. For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over $\mathbb{F}_q$ with Weil polynomial $f$.

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Jeff Achter, Cassie Williams. 2015-05-22. Local heuristics and an exact formula for abelian surfaces over finite fields. https://doi.org/10.4153/cmb-2015-050-8

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