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Let $(R, \mathfrak{m}, k)$ be an excellent equidimensional local ring ofcharacteristic $p>0$. The aim of this paper is to show that$\ell_R(\mathfrak{q}^*/\mathfrak{q})$ does not depend on the choice ofparameter ideal $\mathfrak{q}$ provided $R$ is an $F$-injective local ring thatis $F$-rational on the punctured spectrum.

Tight closure of parameter ideals in local rings $F$-rational on the punctured spectrum