منابع مشابه
Deformation of F-purity and F-regularity
For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.
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It is proved that an excellent local ring of prime characteristic in which a single ideal generated by any system of parameters is tightly closed must be pseu-dorational. A key point in the proof is a characterization of F-rational local rings as those Cohen-Macaulay local rings (R; m) in which the local cohomology module H d m (R) (where d is the dimension of R) have no submodules stable under...
متن کاملGood filtrations and F -purity of invariant subrings
Let k be an algebraically closed field of positive characteristic, G a reductive group over k, and V a finite dimensional G-module. Let B be a Borel subgroup of G, and U its unipotent radical. We prove that if S = SymV has a good filtration, then SU is F -pure. Throughout this paper, p denotes a prime number. Let k be an algebraically closed field of characteristic p, and G a reductive group ov...
متن کاملFailure of F-purity and F-regularity in Certain Rings of Invariants
Let Fq be a finite field of characteristic p, K a field containing it, and R = K[X1, . . . , Xn] a polynomial ring in n variables. The general linear group GLn(Fq) has natural action on R by degree preserving ring automorphisms. L. E. Dickson showed that the subring of elements which are fixed by this group action is a polynomial ring, [Di], though for an arbitrary subgroupG of GLn(Fq), the str...
متن کاملViable singularity-free f(R) gravity without a cosmological constant.
Several authors have argued that self-consistent f(R) gravity models distinct from the cold dark matter model with a cosmological constant (LambdaCDM) are almost ruled out. Confronting such claims, we present a particular two-parameter f(R) model that (a) is cosmologically viable and distinguishable from LambdaCDM, (b) is compatible with the existence of relativistic stars, (c) is free of singu...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1983
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1983-0701505-0