Vol. 10, No. 6, 2016

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On the local Tamagawa number conjecture for Tate motives over tamely ramified fields

Jay Daigle and Matthias Flach

Vol. 10 (2016), No. 6, 1221–1275
Abstract

The local Tamagawa number conjecture, which was first formulated by Fontaine and Perrin-Riou, expresses the compatibility of the (global) Tamagawa number conjecture on motivic L-functions with the functional equation. The local conjecture was proven for Tate motives over finite unramified extensions Kp by Bloch and Kato. We use the theory of (φ,Γ)-modules and a reciprocity law due to Cherbonnier and Colmez to provide a new proof in the case of unramified extensions, and to prove the conjecture for p(2) over certain tamely ramified extensions.

Keywords
Tamagawa number conjecture
Mathematical Subject Classification 2010
Primary: 14F20
Secondary: 11G40, 18F10, 22A99
Milestones
Received: 25 August 2015
Revised: 9 March 2016
Accepted: 18 May 2016
Published: 30 August 2016
Authors
Jay Daigle
Department of Mathematics
Occidental College
1600 Campus Road
Los Angeles, CA 90041
United States
Matthias Flach
Department of Mathematics
Caltech
253/37
Pasadena, CA 91125
United States