共查询到20条相似文献，搜索用时 0 毫秒
1.
Moira A. McDermott 《Proceedings of the American Mathematical Society》1999,127(7):1975-1979
Regular closure is an operation performed on submodules of arbitrary modules over a commutative Noetherian ring. The regular closure contains the tight closure when both are defined, but in general, the regular closure is strictly larger. Regular closure is interesting, in part, because it is defined a priori in all characteristics, including mixed characteristic. We show that one can test regular closure in a Noetherian ring by considering only local maps to regular local rings. In certain cases, it is necessary only to consider maps to certain affine algebras. We also prove the equivalence of two variants of regular closure for a class of rings that includes .
2.
Moira A. McDermott 《Transactions of the American Mathematical Society》2000,352(1):95-114
We consider tight closure, plus closure and Frobenius closure in the rings , where is a field of characteristic and . We use a -grading of these rings to reduce questions about ideals in the quotient rings to questions about ideals in the regular ring . We show that Frobenius closure is the same as tight closure in certain classes of ideals when . Since , we conclude that for these ideals. Using injective modules over the ring , the union of all th roots of elements of , we reduce the question of whether for -graded ideals to the case of -graded irreducible modules. We classify the irreducible -primary -graded ideals. We then show that for most irreducible -primary -graded ideals in , where is a field of characteristic and . Hence for these ideals.
3.
Gennady Lyubeznik Karen E. Smith 《Transactions of the American Mathematical Society》2001,353(8):3149-3180
Let be a reduced ring that is essentially of finite type over an excellent regular local ring of prime characteristic. Then it is shown that the test ideal of commutes with localization and, if is local, with completion, under the additional hypothesis that the tight closure of zero in the injective hull of the residue field of every local ring of is equal to the finitistic tight closure of zero in . It is conjectured that this latter condition holds for all local rings of prime characteristic; it is proved here for all Cohen-Macaulay singularities with at most isolated non-Gorenstein singularities, and in general for all isolated singularities. In order to prove the result on the commutation of the test ideal with localization and completion, a ring of Frobenius operators associated to each -module is introduced and studied. This theory gives rise to an ideal of which defines the non-strongly F-regular locus, and which commutes with localization and completion. This ideal is conjectured to be the test ideal of in general, and shown to equal the test ideal under the hypothesis that in every local ring of .
4.
Pham Huu Tiep A. E. Zalesskii 《Proceedings of the American Mathematical Society》2002,130(11):3177-3184
Let be a finite group of Lie type in characteristic . This paper addresses the problem of describing the irreducible complex (or -adic) representations of that remain absolutely irreducible under the Brauer reduction modulo . An efficient approach to solve this problem for 3$\">has been elaborated in earlier papers by the authors. In this paper, we use arithmetical properties of character degrees to solve this problem for the groups
provided that . We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over with large enough.
provided that . We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over with large enough.
5.
《代数通讯》2013,41(10):3375-3388
We present two applications of a characteristic p analog of multiplier ideals, which is a generalization of the test ideal in the theory of tight closure. Namely, we give alternative proofs to Smith's result on base-point-freeness of adjoint bundles in characteristic p > 0 and results on uniform behavior of symbolic powers in a regular local ring due to Ein, Lazarsfeld and Smith, and Hochster and Huneke. 相似文献
6.
It is shown that tight closure commutes with localization in any two-dimensional ringR of prime characteristic if eitherR is a Nagata ring orR possesses a weak test element. Moreover, it is proved that tight closure commutes with localization at height one prime ideals
in any ring of prime characteristic. 相似文献
7.
Janet Cowden Vassilev 《Transactions of the American Mathematical Society》1998,350(10):4041-4051
Let be an -finite regular local ring and an ideal contained in . Let . Fedder proved that is -pure if and only if . We have noted a new proof for his criterion, along with showing that , where is the pullback of the test ideal for . Combining the the -purity criterion and the above result we see that if is -pure then is also -pure. In fact, we can form a filtration of , that stabilizes such that each is -pure and its test ideal is . To find examples of these filtrations we have made explicit calculations of test ideals in the following setting: Let , where is either a polynomial or a power series ring and is generated by monomials and the are regular. Set . Then .
8.
Alina Carmen Cojocaru 《Transactions of the American Mathematical Society》2003,355(7):2651-2662
Let be an elliptic curve defined over and with complex multiplication. For a prime of good reduction, let be the reduction of modulo We find the density of the primes for which is a cyclic group. An asymptotic formula for these primes had been obtained conditionally by J.-P. Serre in 1976, and unconditionally by Ram Murty in 1979. The aim of this paper is to give a new simpler unconditional proof of this asymptotic formula and also to provide explicit error terms in the formula.
9.
Samuel S. Wagstaff Jr.. 《Mathematics of Computation》1996,65(213):383-391
We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.
10.
Karen E. Smith 《代数通讯》2013,41(12):5915-5929
Abstract For a canonical threefold X, we know that h 0(X, 𝒪 X (nK X )) ≥ 1 for a sufficiently large n. When χ(𝒪 X ) > 0, it is not easy to get such an integer n. Fletcher showed that h 0(X, 𝒪 X (12K X )) ≥ 1 and h 0(X, 𝒪 X (24K X )) ≥ 2 when χ(𝒪 X ) = 1. He inquired about existence of a canonical threefold with given conditions which shows the result sharp. We show that such an example does not exist. Using a different technique, we prove h 0(X, 𝒪 X (12K X )) ≥ 2. 相似文献
11.
Ian M. Aberbach 《Proceedings of the American Mathematical Society》2005,133(1):27-29
Let be an excellent local ring of positive prime characteristic. We show that if , then is regular. This improves a result of Schoutens, in which the additional hypothesis that was an isolated singularity was required for the proof.
12.
Saharon Shelah 《Mathematical Logic Quarterly》2010,56(4):397-399
We prove that, e.g., in (ω 3)(ω 3) there is no sequence of length W4 increasing modulo the ideal of countable sets (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Adela Vraciu 《Proceedings of the American Mathematical Society》2004,132(2):341-346
We study the smallest possible type of tightly closed ideals that are cofinal with the powers of the maximal ideal; this numerical invariant yields information about the tight closure of arbitrary ideals in the ring.
14.
Florian Enescu 《Proceedings of the American Mathematical Society》2003,131(11):3379-3386
The notion of stability of the highest local cohomology module with respect to the Frobenius functor originates in the work of R. Hartshorne and R. Speiser. R. Fedder and K.-i. Watanabe examined this concept for isolated singularities by relating it to -rationality. The purpose of this note is to study what happens in the case of non-isolated singularities and to show how this stability concept encapsulates a few of the subtleties of tight closure theory. Our study can be seen as a generalization of the work by Fedder and Watanabe. We introduce two new ring invariants, the -stability number and the set of -stable primes. We associate to every ideal generated by a system of parameters and an ideal of multipliers denoted and obtain a family of ideals . The set is independent of and consists of finitely many prime ideals. It also equals prime ideal such that is -stable. The maximal height of such primes defines the -stability number.
15.
Donna Glassbrenner 《Proceedings of the American Mathematical Society》1996,124(2):345-353
We characterize strong F-regularity, a property associated with tight closure, in a large class of rings. A special case of our results is a workable criterion in complete intersection rings.
16.
Let (R, m) be a two-dimensional regular local ring and let A be a finitely generated torsion-free R-module. If A is a complete module, then Dan Katz and Vijay Kodiyalam show A satisfies five conditions. They ask whether these five conditions are equivalent without assuming A to be complete. In a previous paper we determined all implications among these five conditions with one exception. In this paper, with an additional hypothesis on the units of R, we resolve the remaining case. 相似文献
17.
Neil M. Epstein 《Proceedings of the American Mathematical Society》2006,134(2):313-321
We prove that if is a flat local homomorphism, is Cohen-Macaulay and -injective, and and share a weak test element, then a tight closure analogue of the (standard) formula for depth and regular sequences across flat base change holds. As a corollary, it follows that phantom depth commutes with completion for excellent local rings. We give examples to show that the analogue does not hold for surjective base change.
18.
《代数通讯》2013,41(11):5447-5471
ABSTRACT The super counterparts of both unital composition algebras and of symmetric composition algebras are classified. It turns out that new objects arise only over fields of characteristic 3. The Principle of Local Triality is considered for this new objects. It is related to some order 3 automorphisms of the simple Liesuperalgebras osp(1,2) and osp(4,2) in characteristic 3. 相似文献
19.
Shigeharu Takayama 《Transactions of the American Mathematical Society》2003,355(1):37-47
We give a new characterization of Iitaka's fibration of algebraic varieties associated to line bundles. Introducing an ``intersection number' of line bundles and curves by using the notion of multiplier ideal sheaves, Iitaka's fibration can be regarded as a ``numerically trivial fibration' in terms of this intersection theory.
20.
David Brink. 《Mathematics of Computation》2007,76(260):2127-2138
For an imaginary quadratic number field and an odd prime number , the anti-cyclotomic -extension of is defined. For primes of , decomposition laws for in the anti-cyclotomic extension are given. We show how these laws can be applied to determine if the Hilbert class field (or part of it) of is -embeddable. For some and , we find explicit polynomials whose roots generate the first step of the anti-cyclotomic extension and show how the prime decomposition laws give nice results on the splitting of these polyniomials modulo . The article contains many numerical examples.