On the local equivariant Tamagawa number conjecture for Tate motives
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911322463010816 |
|---|---|
| author | Atsuta, Mahiro Dainobu, Naoto Kataoka, Takenori |
| author_facet | Atsuta, Mahiro Dainobu, Naoto Kataoka, Takenori |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the local equivariant Tamagawa number conjecture for Tate motives Atsuta, Mahiro Dainobu, Naoto Kataoka, Takenori Number Theory 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. |
| title | On the local equivariant Tamagawa number conjecture for Tate motives |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.14247 |