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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


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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