Root numbers of elliptic curves in residue characteristic 2

Details Root numbers of elliptic curves in residue characteristic 2 Root numbers of elliptic curves in residue characteristic 2

2006-12-02

arxiv.org/abs/math/0612054v1

Mathematics

Number Theory

10 pages

Scientific paper

10.1112/blms/bdn034

To determine the global root number of an elliptic curve defined over a number field, one needs to understand all the local root numbers. These have been classified except at places above 2, and in this paper we attempt to complete the classification. At places above 2, we express the local root numbers in terms of norm residue symbols (resp. root numbers of explicit 1-dimensional characters) in case when wild inertia acts through a cyclic (resp. quaternionic) quotient.

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