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Bulletin of the London Mathematical Society Advance Access originally published online on May 3, 2008
Bulletin of the London Mathematical Society 2008 40(3):516-524; doi:10.1112/blms/bdn034
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© 2008 London Mathematical Society

Root numbers of elliptic curves in residue characteristic 2

Tim Dokchitser

Robinson College
Cambridge
CB3 9AN
United Kingdom

Vladimir Dokchitser

Gonville & Caius College
Cambridge
CB2 1TA
United Kingdom
v.dokchitser@dpmms.cam.ac.uk

Received 10 January 2007. Revision received 18 November 2007.

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 in the case when wild inertia acts through a cyclic quotient, and in terms of root numbers of explicit 1-dimensional characters in the case when wild inertia acts through a quaternionic quotient.

The first author was supported by a Royal Society Research Fellowship.

2000 Mathematics Subject Classification 11G07 (primary) 11F80 (secondary).


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