Frobenius--Witt cotangent complex for derived rings

@misc{mao2026frobeniuswitt,
  title = {{Frobenius--Witt cotangent complex for derived rings}},
  author = {Zhouhang Mao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.04487},
  eprint = {2608.04487},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.04487},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Frobenius--Witt cotangent complex for derived rings
AU  - Zhouhang Mao
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.04487
UR  - https://arxiv.org/abs/2608.04487
AB  - Shimada recently showed that Frobenius--Witt cotangent complex, the animation of Saito's Frobenius--Witt differentials, vanishes on perfectoid rings, thus it serves as a candidate of ``absolute'' cotangent complex. In this article, we give a pullback description of their arithmetic extension, and as a consequence, we give a direct description of Frobenius--Witt cotangent complex, which leads to generalizations to derived rings and animated pre-log rings. This description allows us to compute Frobenius--Witt cotangent complex of derived δ-rings as well. We also propose a version of Frobenius--Witt cotangent complex relative to derived δ-rings, and establish a vanishing result for prisms, which generalizes vanishing of Frobenius--Witt cotangent complex of perfectoid rings. Finally, independently of previous considerations, we give a regularity criterion via Frobenius--Witt cotangent complex for p-local Noetherian (not necessarily local) rings without F-finiteness. We also record the flatness of Frobenius--Witt cotangent complex of valuation rings, with essential ideas due to ChatGPT-6 Astra.
ER  -