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Root numbers and parity of ranks of elliptic curves
-
Tim Dokchitser
and
Vladimir Dokchitser
Published/Copyright:
March 23, 2011
Abstract
The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich–Tate conjecture implies the parity conjecture for all elliptic curves over number fields, we give a formula for local and global root numbers of elliptic curves and complete the proof of a conjecture of Kramer and Tunnell in characteristic 0. The method is to settle the outstanding local formulae by deforming from local fields to totally real number fields and then using global parity results.
Received: 2009-11-02
Revised: 2010-04-25
Published Online: 2011-03-23
Published in Print: 2011-September
© Walter de Gruyter Berlin · New York 2011
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Articles in the same Issue
- K3 surfaces, entropy and glue
- Bäcklund transformations for transparent connections
- Root numbers and parity of ranks of elliptic curves
- Nombres réels de complexité sous-linéaire : mesures d'irrationalité et de transcendance
- On existence of log minimal models II
- Iterated sequences and the geometry of zeros
- Analytic R-groups of affine Hecke algebras
- Strongly free sequences and pro-p-groups of cohomological dimension 2
- Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids
