Kategoria BISAC: Mathematics >> Algebra - Abstract

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics.

To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve...

Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

This monograph presents a review of the basis of operad theory. It also studies structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

The authors develop thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring." Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions.

The reader is assumed to be familiar with general categorical notions, some basic commutative algebra...

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce premier volume du Livre d Algebre commutative, septieme Livre du traite, est consacre aux concepts fondamentaux de l algebre commutative. Il comprend les chapitres: 1. Modules plats; 2. Localisation; 3. Graduations, filtrations et topologies; 4. Ideaux premiers associes et decomposition primaire.

Il contient egalement des notes historiques.

Ce volume est une reimpression de l edition de 1969.

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce deuxieme volume du Livre d Algebre commutative, septieme Livre du traite, introduit deux notions fondamentales en algebre commutative, celle d entier algebrique et celle de valuation, qui ont de nombreuses applications en theorie des nombres et en geometrie algebrique. It traite egalement des anneaux de Krull ou de Dedekind. Il comprend les chapitres: 1. Entiers; 2. Valuations; 3. Diviseurs.

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce volume du Livre d Algebre commutative, septieme Livre du traite, comprend les chapitres: 1. Dimension; 2. Anneaux locaux noetheriens complets.

Le chapitre 8 traite de diverses notions de dimension en algebre commutative, telles que la dimension de Krull d un anneau. Ces notions jouent un role capital en geometrie algebrique. Le chapitre 9 introduit, quant a lui, les vecteurs de Witt et...

This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on "New Techniques in Topological Quantum Field Theory." This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields.

The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N....

Dieses Buch fuhrt kompakt in einige Kerngebiete der Diskreten Mathematik ein. Es behandelt grundlegende Konzepte der Kombinatorik und Graphentheorie und konzentriert sich auf thematische Einheiten wie endliche Geometrien und Ramseytheorie sowie auf methodische Schwerpunkte wie probabilistische und algebraische Techniken. Die Diskrete Mathematik zeigt sich hier als eine spannende Disziplin mit Fragestellungen, die zahlreiche Bezuge zu klassischen Anfangervorlesungen hat. Das Buch ist fur zwei- bis vierstundige Lehrveranstaltungen geeignet.