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Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry

1992 Mathematics
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Release : 1992
Genre : Mathematics
Kind : eBook
Book Rating : 306/5 ( reviews)

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Book Synopsis Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry by : R. Keith Dennis

Download or read book Algebraic $K$-Theory, Commutative Algebra, and Algebraic Geometry written by R. Keith Dennis. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-1960's, several Italian mathematicians began to study the connections between classical arguments in commutative algebra and algebraic geometry, and the contemporaneous development of algebraic K-theory in the US. These connections were exemplified by the work of Andreotti-Bombieri, Salmon, and Traverso on seminormality, and by Bass-Murthy on the Picard groups of polynomial rings. Interactions proceeded far beyond this initial point to encompass Chow groups of singular varieties, complete intersections, and applications of K-theory to arithmetic and real geometry. This volume contains the proceedings from a US-Italy Joint Summer Seminar, which focused on this circle of ideas. The conference, held in June 1989 in Santa Margherita Ligure, Italy, was supported jointly by the Consiglio Nazionale delle Ricerche and the National Science Foundation. The book contains contributions from some of the leading experts in this area.

The Local Structure of Algebraic K-Theory

2012-09-06 Mathematics
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Release : 2012-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 930/5 ( reviews)

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Book Synopsis The Local Structure of Algebraic K-Theory by : Bjørn Ian Dundas

Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas. This book was released on 2012-09-06. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Algebraic K-Theory

2013-11-21 Science
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Release : 2013-11-21
Genre : Science
Kind : eBook
Book Rating : 354/5 ( reviews)

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Book Synopsis Algebraic K-Theory by : Vasudevan Srinivas

Download or read book Algebraic K-Theory written by Vasudevan Srinivas. This book was released on 2013-11-21. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic K-Theory

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 695/5 ( reviews)

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Book Synopsis Algebraic K-Theory by : Hvedri Inassaridze

Download or read book Algebraic K-Theory written by Hvedri Inassaridze. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.

Higher Algebraic K-Theory: An Overview

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 398/5 ( reviews)

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Book Synopsis Higher Algebraic K-Theory: An Overview by : Emilio Lluis-Puebla

Download or read book Higher Algebraic K-Theory: An Overview written by Emilio Lluis-Puebla. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.

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