Twenty-four Hours of Local Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Twenty-four Hours of Local Cohomology write by . This book was released on . Twenty-four Hours of Local Cohomology available in PDF, EPUB and Kindle. This is an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. The text covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, and connections to sheaf cohomology and to de Rham cohomology.
Twenty-Four Hours of Local Cohomology
Twenty-Four Hours of Local Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Twenty-Four Hours of Local Cohomology write by Srikanth B. Iyengar. This book was released on 2022-07-19. Twenty-Four Hours of Local Cohomology available in PDF, EPUB and Kindle. 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.
Twenty-four Hours of Local Cohomology
Twenty-four Hours of Local Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Twenty-four Hours of Local Cohomology write by Srikanth B. Iyengar. This book was released on 2007. Twenty-four Hours of Local Cohomology available in PDF, EPUB and Kindle.
Representations of Finite Groups: Local Cohomology and Support
Representations of Finite Groups: Local Cohomology and Support - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Finite Groups: Local Cohomology and Support write by David J. Benson. This book was released on 2011-11-15. Representations of Finite Groups: Local Cohomology and Support available in PDF, EPUB and Kindle. 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, Čech and Local Homology and Cohomology
Completion, Čech and Local Homology and Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Completion, Čech and Local Homology and Cohomology write by Peter Schenzel. This book was released on 2018-09-15. Completion, Čech and Local Homology and Cohomology available in PDF, EPUB and Kindle. 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.
