Wednesday, March 22
Milner 317, 12:30 PM
Title: Finite orthogonal groups and twists of elliptic curves
Abstract: Let q be an odd prime power, K = F_q(t), and E/K be an elliptic curve with non-constant j-invariant. The L-function of E/K is a polynomial with coefficients in Z, hence a natural question is to ask about the reduction of the L-function modulo a prime l. This question is difficult to answer in general, but for certain families of twists it turns out one can prove theorems about the reduction on average. The key point is to determine the mod-l monodromy of such a family, which a priori is a subgroup of a finite orthogonal group (over Z_l). We'll show that the monodromy group is usually `big' in a strongly uniform way as we vary l and the family of twists of E.