de Rham theory and locally analytic vectors

2026/08/01 by Hui Gao, Gal Porat, Léo Poyeton
Mathematics · #math.NT

paper · pdf

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

Let K_∞/K be a p-adic Lie extension of a p-adic field K. We study the subring of pro-analytic vectors in the de Rham period ring B_dR⁺(K_∞). We show that the pro-analytic subring admits a Galois-equivariant isomorphism with a formal power series ring \widehatK_∞^la [[t_{K_∞}]] if and only if K_∞ satisfies a certain orientability condition, which says that the \widehatK_∞-level Sen operator admits a Galois-equivariant B_dR⁺-lift. A key input is the vanishing of higher locally analytic vectors of \widehatK_∞-representations. As an application, we show that the lifted Sen operator induces regular connections on pro-analytic vectors of B_dR⁺-representations, and can be used to compute Galois cohomology.

Citations

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