Frobenius–Witt differentials and regularity

Saito, Takeshi

doi:10.2140/ant.2022.16.369

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Frobenius–Witt differentials and regularity

Takeshi Saito

Vol. 16 (2022), No. 2, 369–391

DOI: 10.2140/ant.2022.16.369

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 $ℤ_{(p)}$ 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.

Keywords

Frobenius–Witt differentials, regular local rings, cotangent complexes

Mathematical Subject Classification

Primary: 13H05, 13N05

Secondary: 14F10

Milestones

Received: 7 August 2020

Revised: 5 November 2021

Accepted: 24 June 2021

Published: 27 April 2022

Authors

Takeshi Saito
School of Mathematical Sciences University of Tokyo Japan

Vol. 16, No. 2, 2022