Frobenius-Witt differentials and regularity

Abstract

T. Dupuy, E. Katz, J. Rabinoff, 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, L. Ramero. In another article arXiv:2006.00448, we use the sheaf of FW-differentials to define the cotangent bundle and the micro-support of an etale sheaf.

22 pages. In v2, schemes are not used except in the last section. Earlier overlap in arXiv:2006.00448 is removed. An error in Lemma 1.3 pointed out by A. Mathew is corrected in v5

Cited by in corpus (2)

• Syntomic complexes and $p$-adic étale Tate twists
• A Jacobian criterion for nonsingularity in mixed characteristic