A refinement of sharply $F$-pure and strongly $F$-regular pairs
نویسندگان
چکیده
منابع مشابه
F -pure Homomorphisms, Strong F -regularity, and F -injectivity
We discuss Matijevic–Roberts type theorem on strong F -regularity, F -purity, and Cohen–Macaulay F -injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F -purity of homomorphisms using Radu–André homomorphisms, and prove basic properties of it. We also discuss a...
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چکیده ندارد.
15 صفحه اولOn F-pure Thresholds
Using the Frobenius map, we introduce a new invariant for a pair (R, a) of a ring R and an ideal a ⊂ R, which we call the F-pure threshold c(a) of a, and study its properties. We see that the F-pure threshold characterizes several ring theoretic properties. By virtue of Hara and Yoshida’s result [HY], the F-pure threshold c(a) in characteristic zero corresponds to the log canonical threshold lc...
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Using an argument based on an idea of Monsky, we prove the rationality of the F-pure thresholds of curve singularities on a smooth surface defined over a finite field. More generally, we prove in this setting the rationality and discreteness of F-jumping exponents, the smallest positive one of which is the F-pure threshold. We also give a lower bound for F-pure thresholds in the homogeneous case.
متن کاملThe F-valued points of the algebra of strongly regular functions of a Kac-Moody group
Let Gm resp. Gf be the minimal resp. formal Kac-Moody group, associated to a symmetrizable generalized Cartan matrix, over a field F of characteristic 0. Let F [Gm] be the algebra of strongly regular functions on Gm. We denote by Ĝm resp. Ĝf certain monoid completions of Gm resp. Gf , build by using the faces of the Tits cone. We show that there is an action of Ĝf × Ĝf on the spectrum of F-valu...
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2010
ISSN: 1939-2346
DOI: 10.1216/jca-2010-2-1-91