6533b7d5fe1ef96bd126482d

RESEARCH PRODUCT

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

Karl SchwedeKevin TuckerManuel Blickle

subject

Pure mathematicsGeneral Mathematics13A35 13D40 14B05 13H10010102 general mathematicsSubalgebraLocal ringSplitting primeF-regularCommutative Algebra (math.AC)Mathematics - Commutative AlgebraF-signatureF-splitting ratio01 natural sciencesF-pureMathematics - Algebraic GeometryCartier algebra0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsSignature (topology)Algebraic Geometry (math.AG)Mathematics

description

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.

yearjournalcountryeditionlanguage
2012-12-01
http://arxiv.org/abs/1107.1082