Flat morphisms with regular fibers do not preserve -rationality
Eamon Quinlan-Gallego
University of Utah, Salt Lake City, USAAustyn Simpson
University of Michigan, Ann Arbor, USAAnurag K. Singh
University of Utah, Salt Lake City, USA
![Flat morphisms with regular fibers do not preserve $F$-rationality cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-rmi.png&w=3840&q=90)
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. (2024), published online first
DOI 10.4171/RMI/1497