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Parity conjectures for elliptic curves over global fields of positive characteristic

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  04 May 2011

Fabien Trihan  and
Christian Wuthrich
Fabien Trihan
Affiliation:
School of Mathematical Sciences, University Nottingham, Nottingham NG7 2RD, UK (email: fabien.trihan@nottingham.ac.uk)
Christian Wuthrich
Affiliation:
School of Mathematical Sciences, University Nottingham, Nottingham NG7 2RD, UK (email: christian.wuthrich@gmail.com)
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Abstract

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We prove the p-parity conjecture for elliptic curves over global fields of characteristic p>3. We also present partial results on the ℓ-parity conjecture for primes ℓ≠p.

Keywords

parity conjectureelliptic curvesfunction fieldsBirch and Swinnerton-Dyer conjecture

MSC classification

Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G05: Elliptic curves over global fields 11G07: Elliptic curves over local fields
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1105 - 1128
Copyright
Copyright © Foundation Compositio Mathematica 2011

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