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.
Original language | English |
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Pages (from-to) | 35-46 |
Number of pages | 12 |
Journal | Journal für die reine und angewandte Mathematik |
Volume | 2016 |
Issue number | 717 |
Early online date | 25 Mar 2014 |
DOIs | |
Publication status | Published - 1 Aug 2016 |
Keywords
- 11F80 (Primary)
- 14G20
- 11S40
- 11G07
- 11G20
- 11G40 (Secondary)
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Professor Tim Dokchitser
- School of Mathematics - Heilbronn Chair in Algebraic/Arithmetic Geometry
- Pure Mathematics
- Number theory and combinatorics
Person: Academic , Member