Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields

Canadian mathematical bulletin

Cassandra Williams¹  Jeffrey Achter² 

[1] James Madison University, Harrisonburg, VA 22807, USA;Colorado State University, Fort Collins, CO 80523-1874, USA

关键词: abelian surfaces;    finite fields;    random matrices;   

DOI  :  10.4153/CMB-2015-050-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistributionconsiderations, we define, for each prime $ell$, a local factor that measures the relative frequency with which $fmod ell$ occursas thecharacteristic polynomial of a symplectic similitude over $mathbb{F}_ell$. For a certainclass of polynomials, we show that the resulting infinite productcalculates the number of principally polarized abelian surfacesover $mathbb{F}_q$with Weil polynomial $f$.

【 授权许可】

Unknown