Twenty Four Hours Of Local Cohomology

Author : Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther
Publisher : American Mathematical Society
Page : 108 pages
File Size : 54,8 Mb
Release : 2022-07-19
Category : Mathematics
ISBN : 9781470471590

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Twenty-Four Hours of Local Cohomology by Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther Pdf

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.

Author : Srikanth B. Iyengar
Publisher : Unknown
Page : 304 pages
File Size : 48,8 Mb
Release : 2007
Category : Algebra, Homological
ISBN : 1470421178

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Twenty-four Hours of Local Cohomology by Srikanth B. Iyengar Pdf

Author : David J. Benson,Srikanth Iyengar,Henning Krause
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 46,6 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9783034802604

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Representations of Finite Groups: Local Cohomology and Support by David J. Benson,Srikanth Iyengar,Henning Krause Pdf

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 : M. P. Brodmann,R. Y. Sharp
Publisher : Cambridge University Press
Page : 514 pages
File Size : 51,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9780521513630

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Local Cohomology by M. P. Brodmann,R. Y. Sharp Pdf

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 : Gennady Lybeznik
Publisher : CRC Press
Page : 366 pages
File Size : 44,6 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 0824707419

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Local Cohomology and Its Applications by Gennady Lybeznik Pdf

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 : Noé Bárcenas,Fernando Galaz-García,Mónica Moreno Rocha
Publisher : American Mathematical Soc.
Page : 237 pages
File Size : 47,6 Mb
Release : 2016-02-01
Category : Mathematicians
ISBN : 9781470421922

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Mexican Mathematicians Abroad by Noé Bárcenas,Fernando Galaz-García,Mónica Moreno Rocha Pdf

This volume contains the proceedings of the First Workshop “Matemáticos Mexicanos Jóvenes en el Mundo”, held from August 22–24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. - See more at: http://bookstore.ams.org/conm-657/#sthash.cUjwTcvX.dpuf This volume contains the proceedings of the First Workshop "Matemáticos Mexicanos Jóvenes en el Mundo", held from August 22-24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields. This book is published in cooperation with Sociedad Matemática Mexicana.

Author : Peter Schenzel,Anne-Marie Simon
Publisher : Springer
Page : 346 pages
File Size : 41,8 Mb
Release : 2018-09-15
Category : Mathematics
ISBN : 9783319965178

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Completion, Čech and Local Homology and Cohomology by Peter Schenzel,Anne-Marie Simon Pdf

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 : Irena Peeva
Publisher : Springer Nature
Page : 898 pages
File Size : 44,5 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030896942

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Commutative Algebra by Irena Peeva Pdf

This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud's 65th birthday. It brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Category Theory, Combinatorics, Computational Algebra, Homological Algebra, Hyperplane Arrangements, and Non-commutative Algebra. The book aims to showcase the area and aid junior mathematicians and researchers who are new to the field in broadening their background and gaining a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.

Author : Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev
Publisher : Walter de Gruyter
Page : 377 pages
File Size : 49,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9783110250404

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Progress in Commutative Algebra 1 by Christopher Francisco,Lee C. Klingler,Sean Sather-Wagstaff,Janet C. Vassilev Pdf

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics. Specifically, one can use combinatorial techniques to investigate resolutions and other algebraic structures as with the papers of Fløystad on Boij-Söderburg theory, of Geramita, Harbourne and Migliore, and of Cooper on Hilbert functions, of Clark on minimal poset resolutions and of Mermin on simplicial resolutions. One can also utilize algebraic invariants to understand combinatorial structures like graphs, hypergraphs, and simplicial complexes such as in the paper of Morey and Villarreal on edge ideals. Homological techniques have become indispensable tools for the study of noetherian rings. These ideas have yielded amazing levels of interaction with other fields like algebraic topology (via differential graded techniques as well as the foundations of homological algebra), analysis (via the study of D-modules), and combinatorics (as described in the previous paragraph). The homological articles the editors have included in this volume relate mostly to how homological techniques help us better understand rings and singularities both noetherian and non-noetherian such as in the papers by Roberts, Yao, Hummel and Leuschke.

Author : Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón
Publisher : Springer
Page : 201 pages
File Size : 55,7 Mb
Release : 2013-08-24
Category : Mathematics
ISBN : 9783642387425

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Monomial Ideals, Computations and Applications by Anna M. Bigatti,Philippe Gimenez,Eduardo Sáenz-de-Cabezón Pdf

This work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.

Author : Burt Totaro
Publisher : Cambridge University Press
Page : 245 pages
File Size : 44,5 Mb
Release : 2014-06-26
Category : Mathematics
ISBN : 9781107015777

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Group Cohomology and Algebraic Cycles by Burt Totaro Pdf

This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

Author : Anonim
Publisher : Cambridge University Press
Page : 248 pages
File Size : 42,9 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 8210379456XXX

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Algebraic Theory of Differential Equations by Anonim Pdf

Author : Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis
Publisher : Springer
Page : 430 pages
File Size : 48,8 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9789811016516

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Algebra and its Applications by Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis Pdf

This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15–17, 2014. The book also includes papers from mathematicians who couldn't attend the conference. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions.

Author : Nicholas R. Baeth,Thiago H. Freitas,Graham J. Leuschke,Victor H. Jorge Pérez
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 51,8 Mb
Release : 2021-10-06
Category : Education
ISBN : 9781470456016

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Commutative Algebra: 150 Years with Roger and Sylvia Wiegand by Nicholas R. Baeth,Thiago H. Freitas,Graham J. Leuschke,Victor H. Jorge Pérez Pdf

This volume contains the combined Proceedings of the Second International Meeting on Commutative Algebra and Related Areas (SIMCARA) held from July 22–26, 2019, at the Universidade de São Paulo, São Carlos, Brazil, and the AMS Special Session on Commutative Algebra, held from September 14–15, 2019, at the University of Wisconsin-Madison, Wisconsin. These two meetings celebrated the combined 150th birthday of Roger and Sylvia Wiegand. The Wiegands have been a fixture in the commutative algebra community, as well as the wider mathematical community, for over 40 years. Articles in this volume cover various areas of factorization theory, homological algebra, ideal theory, representation theory, homological rigidity, maximal Cohen-Macaulay modules, and the behavior of prime spectra under completion, as well as some topics in related fields. The volume itself bears evidence that the area of commutative algebra is a vibrant one and highlights the influence of the Wiegands on generations of researchers. It will be useful to researchers and graduate students.

Author : Summer School on Interactions between Homotopy Theory and Algebra
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 43,5 Mb
Release : 2007
Category : Commutative algebra
ISBN : 9780821838143

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Interactions between Homotopy Theory and Algebra by Summer School on Interactions between Homotopy Theory and Algebra Pdf

This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.