Vol. 16, No. 2, 2022

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Frobenius–Witt differentials and regularity

Takeshi Saito

Vol. 16 (2022), No. 2, 369–391

T. Dupuy, E. Katz, J. Rabinoff, and D. Zureick-Brown introduced the module of total p-differentials for a ring over p2. We study the same construction for a ring over (p) and prove a regularity criterion. For a local ring, the tensor product with the residue field is constructed in a different way by O. Gabber and L. Ramero.

In another article we use the sheaf of FW-differentials to define the cotangent bundle and the microsupport of an étale sheaf.

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Frobenius–Witt differentials, regular local rings, cotangent complexes
Mathematical Subject Classification
Primary: 13H05, 13N05
Secondary: 14F10
Received: 7 August 2020
Revised: 5 November 2021
Accepted: 24 June 2021
Published: 27 April 2022
Takeshi Saito
School of Mathematical Sciences
University of Tokyo