5,132 research outputs found
Interface between astrophysical datasets and distributed database management systems (DAVID)
This is a status report on the progress of the DAVID (Distributed Access View Integrated Database Management System) project being carried out at Louisiana State University, Baton Rouge, Louisiana. The objective is to implement an interface between Astrophysical datasets and DAVID. Discussed are design details and implementation specifics between DAVID and astrophysical datasets
Gorenstein algebras and Hochschild cohomology
For homomorphism K-->S of commutative rings, where K is Gorenstein and S is
essentially of finite type and flat as a K-module, the property that all
non-trivial fiber rings of K-->S are Gorenstein is characterized in terms of
properties of the cohomology modules Ext_n^{S\otimes_KS}S{S\otimes_KS}.Comment: This is the published version, except for updates to references and
bibliography. Sections 3, 4 and 8 have been removed from the preceding
version, arXiv:0704.3761v2. Substantial generalizations of results in those
sections are proved in our paper with Joseph Lipman and Suresh Nayak,
arXiv:0904.400
Duality in algebra and topology
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that
they can be extended to the more general rings that come up in homotopy theory.
Amongst the rings we work with are the differential graded ring of cochains on a space, the differential graded ring of chains on the loop space, and various ring spectra, e.g., the Spanier-Whitehead duals of finite spectra or chromatic localizations of the sphere spectrum.
Maybe the most important contribution of this paper is the conceptual framework, which allows us to view all of the following dualities: Poincare duality for manifolds, Gorenstein duality for commutative rings, Benson-Carlson duality for cohomology rings of finite groups, Poincare duality for groups, Gross-Hopkins duality in chromatic stable homotopy theory, as examples of a single phenomenon. Beyond setting up this framework, though, we prove some new results, both in algebra and topology, and give new proofs of a number of old results
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