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arXiv · 2302.09744

Local epsilon conjecture and p-adic differential equations

Tetsuya Ishida·Kentaro Nakamura
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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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Tetsuya Ishida, Kentaro Nakamura. 2023-02-26. Local epsilon conjecture and p-adic differential equations. https://arxiv.org/abs/2302.09744

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