Root numbers and parity of ranks of elliptic curves

TY Dokchitser, V Dokchitser

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

21 Citations (Scopus)


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.
Translated title of the contributionRoot numbers and parity of ranks of elliptic curves
Original languageEnglish
Pages (from-to)39 - 64
Number of pages26
JournalJournal für die reine und angewandte Mathematik
Issue number658
Publication statusPublished - 23 Mar 2011

Bibliographical note

Publisher: de Gruyter

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