Local Cohomology
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Local Cohomology And Its Applications
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Author : Gennady Lybeznik
language : en
Publisher: CRC Press
Release Date : 2001-10-18
Local Cohomology And Its Applications written by Gennady Lybeznik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-18 with Mathematics categories.
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.
Local Cohomology
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Author : Robin Hartshorne
language : en
Publisher: Springer
Release Date : 2006-11-14
Local Cohomology written by Robin Hartshorne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Local Cohomology
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Author : M. P. Brodmann
language : en
Publisher: Cambridge University Press
Release Date : 2013
Local Cohomology written by M. P. Brodmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.
Twenty Four Hours Of Local Cohomology
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Author : Srikanth B. Iyengar
language : en
Publisher: American Mathematical Society
Release Date : 2022-07-19
Twenty Four Hours Of Local Cohomology written by Srikanth B. Iyengar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-19 with Mathematics categories.
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Representations Of Finite Groups Local Cohomology And Support
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Author : David J. Benson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-15
Representations Of Finite Groups Local Cohomology And Support written by David J. Benson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.
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.
Completion Ech And Local Homology And Cohomology
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Author : Peter Schenzel
language : en
Publisher: Springer
Release Date : 2018-09-15
Completion Ech And Local Homology And Cohomology written by Peter Schenzel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-15 with Mathematics categories.
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.
Local Cohomology
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Author : Robin Hartshorne
language : en
Publisher:
Release Date : 2014-01-15
Local Cohomology written by Robin Hartshorne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Local Cohomology
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Author : Markus P. Brodmann
language : en
Publisher:
Release Date : 2013
Local Cohomology written by Markus P. Brodmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Algebra, Homological categories.
Local Cohomology Second Edition
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Author : M. P. Brodmann. R. Y. Sharp
language : en
Publisher:
Release Date : 2012
Local Cohomology Second Edition written by M. P. Brodmann. R. Y. Sharp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Local Cohomology And Localization
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Author : José Luis Bueso
language : en
Publisher: Longman Scientific and Technical
Release Date : 1989
Local Cohomology And Localization written by José Luis Bueso and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Homology theory categories.