English

On Quasi-$F$-Purity of Excellent Rings

Commutative Algebra 2025-09-30 v2 Algebraic Geometry

Abstract

We introduce an analogue to Quasi-FF-splittings, Quasi-FF-purity, which is definable over rings that are not necessarily FF-finite. We show that this property is equivalent to being Quasi-FF-split in the complete local and FF-finite case. We then exhibit that it is stable under completion, direct limit, and local/finite \'etale extension.

Keywords

Cite

@article{arxiv.2503.10778,
  title  = {On Quasi-$F$-Purity of Excellent Rings},
  author = {Vignesh Jagathese},
  journal= {arXiv preprint arXiv:2503.10778},
  year   = {2025}
}

Comments

Final version, to appear in Communications in Algebra LAGB