location:  Publications → journals
Search results

Search: MSC category 14K02 ( Isogeny )

 Expand all        Collapse all Results 1 - 2 of 2

1. CMB 2015 (vol 58 pp. 673)

Achter, Jeffrey; Williams, Cassandra
 Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistribution considerations, we define, for each prime $\ell$, a local factor that 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 $f$. Keywords:abelian surfaces, finite fields, random matricesCategory:14K02

2. CMB 2001 (vol 44 pp. 313)

 Images of mod $p$ Galois Representations Associated to Elliptic Curves We give an explicit recipe for the determination of the images associated to the Galois action on $p$-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over $\QQ$ without complex multiplication with conductor less than 200 and for each prime number~$p$. Keywords:Galois groups, elliptic curves, Galois representation, isogenyCategories:11R32, 11G05, 12F10, 14K02