Frobenius--Witt cotangent complexes

@misc{shimada2026frobeniuswitt,
  title = {{Frobenius--Witt cotangent complexes}},
  author = {Kanau Shimada},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2605.14803},
  eprint = {2605.14803},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.14803},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Frobenius--Witt cotangent complexes
AU  - Kanau Shimada
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2605.14803
UR  - https://arxiv.org/abs/2605.14803
AB  - We introduce the notion of the Frobenius--Witt cotangent complex, which can be considered as a derived variant of the module of Frobenius--Witt differentials defined by T. Saito. This new object also can be seen as an arithmetic variant of the notion of cotangent complex. We explain the suitability of these two viewpoints through a series of propositions. Furthermore, we establish a relationship between Frobenius--Witt cotangent complexes and the regularity of noetherian local rings, which can be considered as a derived variant of Saito's regularity criterion. This proof relies heavily on computations of Frobenius--Witt cotangent complexes in the case of perfectoid rings. We also study the deformation theory of delta structures using Frobenius--Witt cotangent complexes.
ER  -