Geodesic
Local $\varepsilon$-conjecture and $p$-adic differential equations
Documenta mathematica, Tome 29 (2024) no. 5, pp. 1125-1156 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Laurent Berger attached a p-adic differential equation Nrig​(M) with a Frobenius structure to an arbitrary de Rham (φ,Γ)-module M over a Robba ring. In this article, we compare the local epsilon conjecture for the cyclotomic deformation of M with that of Nrig​(M). We first define an isomorphism between the fundamental lines of their cyclotomic deformations using the second author’s results on the big exponential map. As a main result of the article, we show that this isomorphism enables us to reduce the local epsilon conjecture for the cyclotomic deformation of M to that of Nrig​(M). The result can be regarded as a refined interpolation formula of the big exponential map.
DOI : 10.4171/dm/973
Classification : 11F80, 11F85, 11R23
Mots-clés : p-adic Hodge theory, (φ,Γ)-module, Bloch–Kato’s exponential, Perrin-Riou’s exponential 
@article{10_4171_dm_973,
     author = {Tetsuya Ishida and Kentaro Nakamura},
     title = {Local $\varepsilon$-conjecture and $p$-adic differential equations},
     journal = {Documenta mathematica},
     pages = {1125--1156},
     year = {2024},
     volume = {29},
     number = {5},
     doi = {10.4171/dm/973},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/973/}
}
TY  - JOUR
AU  - Tetsuya Ishida
AU  - Kentaro Nakamura
TI  - Local $\varepsilon$-conjecture and $p$-adic differential equations
JO  - Documenta mathematica
PY  - 2024
SP  - 1125
EP  - 1156
VL  - 29
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/973/
DO  - 10.4171/dm/973
ID  - 10_4171_dm_973
ER  - 
%0 Journal Article
%A Tetsuya Ishida
%A Kentaro Nakamura
%T Local $\varepsilon$-conjecture and $p$-adic differential equations
%J Documenta mathematica
%D 2024
%P 1125-1156
%V 29
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/973/
%R 10.4171/dm/973
%F 10_4171_dm_973
Tetsuya Ishida; Kentaro Nakamura. Local $\varepsilon$-conjecture and $p$-adic differential equations. Documenta mathematica, Tome 29 (2024) no. 5, pp. 1125-1156. doi: 10.4171/dm/973

Cité par Sources :