𝐹-thresholds of hypersurfaces

Blickle, Manuel; Mustaţǎ, Mircea; Smith, Karen

doi:10.1090/S0002-9947-09-04719-9

$F$-thresholds of hypersurfaces
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by Manuel Blickle, Mircea Mustaţǎ and Karen E. Smith PDF

Trans. Amer. Math. Soc. 361 (2009), 6549-6565 Request permission

Abstract:

We use the $D$-module theoretic description of generalized test ideals to show that in any $F$-finite regular ring the $F$-thresholds of hypersurfaces are discrete and rational. Furthermore we show that any limit of $F$-pure thresholds of principal ideals in bounded dimension is again an $F$-pure threshold; hence in particular the limit is rational.

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