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Published August 30, 2016 | Submitted
Journal Article Open

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

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 K∕ℚ_p 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 ℚ_p(2) over certain tamely ramified extensions.

Additional Information

© 2016 Mathematical Sciences Publishers. Received: 25 August 2015. Revised: 9 March 2016. Accepted: 18 May 2016. Published: 30 August 2016. Communicated by Kiran S. Kedlaya. We would like to thank the referee for a very careful reading of the manuscript, which helped to improve our exposition a lot.

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