Local epsilon conjecture and p-adic differential equations

2023/02/20 by Tetsuya Ishida, Kentaro Nakamura, Ishida, Tetsuya +1
Mathematics · Medicine · #Algebraic Geometry and Number Theory #Berberine and alkaloids research #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.09744

openalex publication_date 2023/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Laurent Berger attached a p-adic differential equation N_rig(M) with a Frobenius structure to an arbitrary de Rham (phi, Gamma)-module over a Robba ring. In this article, we compare the local epsilon conjecture for the cyclotomic deformation of M with that of N_rig(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 N_rig(M).

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