Frobenius-Witt differentials and regularity
Algebraic Geometry
2024-10-08 v5 Commutative Algebra
Number Theory
Abstract
T. Dupuy, E. Katz, J. Rabinoff, D. Zureick-Brown introduced the module of total -differentials for a ring over . We study the same construction for a ring over 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.
Cite
@article{arxiv.2008.04728,
title = {Frobenius-Witt differentials and regularity},
author = {Takeshi Saito},
journal= {arXiv preprint arXiv:2008.04728},
year = {2024}
}
Comments
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