Auslander regularity of completed rings of $p$-adic differential operators

Andreas Bode

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arXiv · 2505.08001

Auslander regularity of completed rings of $p$-adic differential operators

Andreas Bode

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Abstract

We prove that any smooth rigid analytic variety $X$ admits an affinoid covering $\{U_i\}$ such that the Banach algebras involved in the Fr\'echet--Stein presentation of the completed ring of differential operators D-cap$(U_i)$ are Auslander regular for each $i$. We use this result to prove projection formulae and adjunction results for coadmissible D-cap-modules.

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Andreas Bode. 2025-05-12. Auslander regularity of completed rings of $p$-adic differential operators. https://arxiv.org/abs/2505.08001

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