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Author : Toma Albu,Constantin Năstăsescu
Publisher : Unknown
Page : 48 pages
File Size : 46,8 Mb
Release : 1979
Category : Commutative rings
ISBN : UVA:X001468463
Author : David J. Benson,Srikanth Iyengar,Henning Krause
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 49,8 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9783034802604
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Author : A. Verschoren
Publisher : EDITUM
Page : 100 pages
File Size : 44,8 Mb
Release : 1990
Category : Mathematics
ISBN : 8476849346
Author : Gennady Lybeznik
Publisher : CRC Press
Page : 366 pages
File Size : 51,5 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 0824707419
This volume collects presentations from the international workshop on local cohomology held in Guanajuato, Mexico, including expanded lecture notes of two minicourses on applications in equivariant topology and foundations of duality theory, and chapters on finiteness properties, D-modules, monomial ideals, combinatorial analysis, and related topics. Featuring selected papers from renowned experts around the world, Local Cohomology and Its Applications is a provocative reference for algebraists, topologists, and upper-level undergraduate and graduate students in these disciplines.
Author : Robert Ray Bruner,John Patrick Campbell Greenlees
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 53,8 Mb
Release : 2003
Category : Algebraic topology
ISBN : 9780821833667
Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
Author : M. P. Brodmann,R. Y. Sharp
Publisher : Cambridge University Press
Page : 514 pages
File Size : 40,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9780521513630
On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.
Author : Peter Schenzel,Anne-Marie Simon
Publisher : Springer
Page : 346 pages
File Size : 46,6 Mb
Release : 2018-09-15
Category : Mathematics
ISBN : 9783319965178
The aim of the present monograph is a thorough study of the adic-completion, its left derived functors and their relations to the local cohomology functors, as well as several completeness criteria, related questions and various dualities formulas. A basic construction is the Čech complex with respect to a system of elements and its free resolution. The study of its homology and cohomology will play a crucial role in order to understand left derived functors of completion and right derived functors of torsion. This is useful for the extension and refinement of results known for modules to unbounded complexes in the more general setting of not necessarily Noetherian rings. The book is divided into three parts. The first one is devoted to modules, where the adic-completion functor is presented in full details with generalizations of some previous completeness criteria for modules. Part II is devoted to the study of complexes. Part III is mainly concerned with duality, starting with those between completion and torsion and leading to new aspects of various dualizing complexes. The Appendix covers various additional and complementary aspects of the previous investigations and also provides examples showing the necessity of the assumptions. The book is directed to readers interested in recent progress in Homological and Commutative Algebra. Necessary prerequisites include some knowledge of Commutative Algebra and a familiarity with basic Homological Algebra. The book could be used as base for seminars with graduate students interested in Homological Algebra with a view towards recent research.
Author : José Luis Bueso,A. Verschoren,Blas Torrecillas
Publisher : Longman Scientific and Technical
Page : 284 pages
File Size : 50,9 Mb
Release : 1989
Category : Homology theory
ISBN : UCAL:B4406130
Author : Jose L. Bueso,Pascual Jara,Blas Torrecillas
Publisher : Springer
Page : 343 pages
File Size : 48,6 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540392781
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
Author : Anonim
Publisher : Unknown
Page : 1020 pages
File Size : 48,6 Mb
Release : 1992
Category : Mathematics
ISBN : CORNELL:31924064492113
Author : Robert Ray Bruner,John Patrick Campbell Greenlees
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 43,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821851890
Focusing on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it, the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory.
Author : M. P. Brodmann,R. Y. Sharp
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,8 Mb
Release : 2012-11-15
Category : Mathematics
ISBN : 9781139788649
This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum–Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton–Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over 300 exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.
Author : Jonathan S. Golan
Publisher : Longman Scientific and Technical
Page : 680 pages
File Size : 43,8 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015015616470
Author : Karl H. Hofmann,Paul S. Mostert
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642806704
Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.
Author : Lance W. Small
Publisher : Unknown
Page : 712 pages
File Size : 44,7 Mb
Release : 1986
Category : Mathematics
ISBN : UCAL:B4342564