Equivariant Tamagawa number conjecture (ETNC)

introduction

The local Tamagawa number conjecure, 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 $K/\mathbb{Q}_p$ by Bloch and Kato.

Olivier Fouquet, $p$-adic properties of motivic fundamental lines (Kato's conjecture is (probably) false for (not so) trivial reasons), arXiv:1604.06413 [math.NT], April 21 2016, http://arxiv.org/abs/1604.06413
Olivier Fouquet, The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras, arXiv:1604.06411 [math.NT], April 21 2016, http://arxiv.org/abs/1604.06411
Daigle, Jay, and Matthias Flach. “On the Local Tamagawa Number Conjecture for Tate Motives over Tamely Ramified Fields.” arXiv:1508.06031 [math], August 25, 2015. http://arxiv.org/abs/1508.06031.
Burns, David, Masato Kurihara, and Takamichi Sano. “Iwasawa Theory and Zeta Elements for $\mathbb{G}_m$.” arXiv:1506.07935 [math], June 25, 2015. http://arxiv.org/abs/1506.07935.