On the local equivariant Tamagawa number conjecture for Tate motives

2025/12/16 by Mahiro Atsuta, Atsuta, Mahiro, Naoto Dainobu +3
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2512.14247

openalex publication_date 2025/12/16 · openalex created_date 2025/12/18 · openalex updated_date 2026/07/28

Abstract

The local equivariant Tamagawa number conjecture (local ETNC) for a motive predicts a precise relationship between the local arithmetic complex and the root numbers which appear in the (conjectural) functional equations of the L-functions. In this paper, we prove the local ETNC for the Tate motives under a certain unramified condition at p. Our result gives a generalization of the previous works by Burns--Flach and Burns--Sano. Our strategy basically follows those works and builds upon the classical theory of Coleman maps and its generalization by Perrin-Riou.

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