$\mathbf{F}$-jumping numbers can be irrational

Abstract

Let $k$ be an $F$-finite and infinite field of characteristic $p>2$. We show, there exist infinitely many $F$-finite local domains $(R,\mathfrak{m})$ which are not $\mathbb{Q}$-Gorenstein and $\ddot{I}{„}_{\mathrm{b}}(R;{\mathfrak{m}}^t)$ has all but finitely many \emph{irrational} $F$-jumping numbers.

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