Root numbers of elliptic curves in residue characteristic 2

Abstract

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.

10 pages

References in corpus (1)

• Parity of ranks for elliptic curves with a cyclic isogeny

Cited by in corpus (7)

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• The remaining cases of the Kramer-Tunnell conjecture