Euler factors determine local Weil representations
Number Theory
2011-12-22 v1
Abstract
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.
Cite
@article{arxiv.1112.4889,
title = {Euler factors determine local Weil representations},
author = {Tim Dokchitser and Vladimir Dokchitser},
journal= {arXiv preprint arXiv:1112.4889},
year = {2011}
}
Comments
12 pages