Euler factors determine local Weil representations

Details Euler factors determine local Weil representations Euler factors determine local Weil representations

2011-12-20

arxiv.org/abs/1112.4889v1

Mathematics

Number Theory

12 pages

Scientific paper

We show that a Frobenius-semisimple Weil representation over a local field K is determined by its Euler factors over the extensions of K. The construction is explicit, and we illustrate it for l-adic representations attached to elliptic and genus 2 curves. As an application, we construct an absolutely simple 2-dimensional abelian variety over Q all of whose quadratic twists must have positive rank, according to the Birch-Swinnerton-Dyer conjecture.

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