#### Vol. 16, No. 2, 2022

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Frobenius–Witt differentials and regularity

### Takeshi Saito

Vol. 16 (2022), No. 2, 369–391
##### Abstract

T. Dupuy, E. Katz, J. Rabinoff, and D. Zureick-Brown introduced the module of total $p$-differentials for a ring over $ℤ∕{p}^{2}ℤ$. We study the same construction for a ring over ${ℤ}_{\left(p\right)}$ 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.

##### Keywords
Frobenius–Witt differentials, regular local rings, cotangent complexes
##### Mathematical Subject Classification
Primary: 13H05, 13N05
Secondary: 14F10