Euler factors determine local Weil representations

Tim Y Dokchitser, Vladimir Dokchitser

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
292 Downloads (Pure)

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 languageEnglish
Pages (from-to)35-46
Number of pages12
JournalJournal für die reine und angewandte Mathematik
Volume2016
Issue number717
Early online date25 Mar 2014
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • 11F80 (Primary)
  • 14G20
  • 11S40
  • 11G07
  • 11G20
  • 11G40 (Secondary)

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