F-signature of pairs and the asymptotic behavior of Frobenius splittings

By Manuel Blickle, Karl Schwede, Kevin Tucker. 2011

58 citations recorded by the source corpus.

We generalize $F$-signature to pairs $(R,D)$ where $D$ is a Cartier subalgebra on $R$ as defined by the first two authors. In particular, we show the existence and positivity of the $F$-signature for any strongly $F$-regular pair. In one application, we answer an open question of I. Aberbach and F. Enescu by showing that the $F$-splitting ratio of an arbitrary $F$-pure local ring is strictly positive. Furthermore, we derive effective methods for computing the $F$-signature and the $F$-splitting ratio in the spirit of the work of R. Fedder.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/59454d7969487cd8ce1f63f799233bcd766929c3

Citations in the corpus

• F-signature and Hilbert–Kunz multiplicity : a combined approach and comparison (2016, unknown): “Previous work of the second author [Blickle et al. 2012; 2013] has extended the notion of F -signature to these settings and beyond, incorporating the notion of a Cartier subalgebra [Blickle and Schwede 2013].”