Flat morphisms with regular fibers do not preserve -rationality

  • Eamon Quinlan-Gallego

    University of Utah, Salt Lake City, USA
  • Austyn Simpson

    University of Michigan, Ann Arbor, USA
  • Anurag K. Singh

    University of Utah, Salt Lake City, USA
Flat morphisms with regular fibers do not preserve $F$-rationality cover
Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

For each prime integer , we construct a standard graded -rational ring , over a field of characteristic , such that is not -rational. By localizing, we obtain a flat local homomorphism such that is -rational, is regular (in fact, a field), but is not -rational. In the process, we also obtain standard graded -rational rings for which is not -rational.

Cite this article

Eamon Quinlan-Gallego, Austyn Simpson, Anurag K. Singh, Flat morphisms with regular fibers do not preserve -rationality. Rev. Mat. Iberoam. 40 (2024), no. 5, pp. 1989–2001

DOI 10.4171/RMI/1497