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Root numbers of elliptic curves in residue characteristic 2
Author(s) -
Dokchitser Tim,
Dokchitser Vladimir
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn034
Subject(s) - quotient , mathematics , root (linguistics) , inertia , residue (chemistry) , elliptic curve , rational number , pure mathematics , norm (philosophy) , root of unity , physics , chemistry , philosophy , linguistics , biochemistry , classical mechanics , quantum mechanics , political science , law , quantum
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.