$F$-injectivity does not deform

Karl Schwede, Austyn Simpson

arXiv:2608.15470v1 Primary: math.AC Secondary: math.AG

Abstract

We show that there exists an $F$-finite four-dimensional local domain $(R,\mathfrak{m})$ of characteristic two which is not $F$-injective but which admits a nonzerodivisor $f\in \mathfrak{m}$ such that $R/fR$ is $F$-injective.

Disclosure

“vel Support for Mathematicians SFI-MPSTSM-00013051. AI Disclosure. This example was found by OpenAI’s ChatGPT 5.6 Sol Pro using a ChatGPT account provided to Karl Schwede by the University of Utah. It was found first in a discussion where ChatGPT 5.6 Sol Pro had already identified some counter-examples to related problems (which will be written up in a separate work). All writing in this article was done by the human authors. Most, but not all, steps in the proof of the main result”
PDF page 2

Classification: Substantial mathematical content or result generation
Multiplier: 10
Verified: 2026-08-23T05:18:08.111358Z

Structural counts

Pages 19 pdf

Theorems 3 source

Lemmas 12 source

Propositions 3 source

Corollaries 4 source

Definitions 1 source

Displayed equations 101 source

Bibliography entries 36 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file CounterExample-FInjDef.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.