Frobenius--Witt cotangent complexes

Kanau Shimada

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arXiv · 2605.14803

Frobenius--Witt cotangent complexes

Kanau Shimada

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Abstract

We introduce the notion of the Frobenius--Witt cotangent complex, which can be considered as a derived variant of the module of Frobenius--Witt differentials defined by T. Saito. This new object also can be seen as an arithmetic variant of the notion of cotangent complex. We explain the suitability of these two viewpoints through a series of propositions. Furthermore, we establish a relationship between Frobenius--Witt cotangent complexes and the regularity of noetherian local rings, which can be considered as a derived variant of Saito's regularity criterion. This proof relies heavily on computations of Frobenius--Witt cotangent complexes in the case of perfectoid rings. We also study the deformation theory of delta structures using Frobenius--Witt cotangent complexes.

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Kanau Shimada. 2026-05-14. Frobenius--Witt cotangent complexes. https://arxiv.org/abs/2605.14803

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