Flat morphisms with regular fibers do not preserve F-rationality

2023/07/07 by Quinlan-Gallego, Eamon, Simpson, Austyn, Singh, Anurag K. · 2 citations
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.03785

Abstract

For each positive prime integer p we construct a standard graded F-rational ring R, over a field K of characteristic p, such that R⊗_KK is not F-rational. By localizing we obtain a flat local homomorphism (R, \mathfrakm) → (S, \mathfrakn) such that R is F-rational, S/\mathfrakm S is regular (in fact, a field), but S is not F-rational. In the process we also obtain standard graded F-rational rings R for which R⊗_K R is not F-rational.

Cited by

• Bertini's theorem for F-rational F-pure singularities
• F-injectivity does not imply F-fullness in normal domains

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