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Friday, April 17, 2020 | History

2 edition of Algebraic K-theory found in the catalog.

Algebraic K-theory

Richard G. Swan

Algebraic K-theory

  • 133 Want to read
  • 22 Currently reading

Published by Springer in Berlin, Heidelberg, New York .
Written in English

    Subjects:
  • Categories (Mathematics),
  • K-theory.

  • Edition Notes

    Includes bibliographical references and index.

    StatementR.G. Swan.
    SeriesLecture notes in mathematics -- 76, Lecture notes in mathematics (Springer-Verlag) -- 76.
    Classifications
    LC ClassificationsQA3 .L28 no. 76
    The Physical Object
    Pagination262 p. :
    Number of Pages262
    ID Numbers
    Open LibraryOL17934745M

    Download Limit Exceeded You have exceeded your daily download allowance.


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Algebraic K-theory by Richard G. Swan Download PDF EPUB FB2

Algebraic K-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher K-groups and to perform menards.club by: 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 menards.club by: Buy Algebraic K-Theory (Lecture Notes Algebraic K-theory book Mathematics) on menards.club FREE SHIPPING on qualified ordersCited by: I talked to Hy Bass, the author of the classic book Algebraic K-theory, about what would be involved in writing such a book.

It was scary, because (in ) I didn't know even how to write a book. I needed a warm-up exercise, a practice book if you will. The result, An introduction to homological algebra, took over five years to write. Jan 30,  · Speaking somewhat loosely, algebraic K-theory could be viewed as an attempt to generalize the invariants of linear algebra (such as determinants and canonical forms) to the case of projective menards.club by: Algebraic K-Theory has become an increasingly active area of research.

With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author'sAuthor: Vasudevan Srinivas.

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. Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory.

The broad range of these topics has tended to give the subject an aura of inapproachability. This book Brand: Springer-Verlag New York.

Lectures On K theory. This book covers the following topics: Topological K-Theory, Topological Preliminaries on Vector Bundles, Homotopy, Bott Periodicity and Cohomological Properties, Chern Character and Chern Classes, Analytic K-Theory, Applications of Adams operations, Higher Algebraic K-Theory, Algebraic Preliminaries and the the Grothendieck Group, The Whitehead and the Steinberg.

Introduction To K theory and Some Applications. This book explains the following topics: Topological K-theory, K-theory of C* Algebraic K-theory book, Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1 of Orders and Group-rings, Higher Algebraic K-theory, Higher Dimensional Class Groups of Orders and Group rings, Higher K-theory of Schemes, Mod-m Higher K-theory of exact Categories, Schemes.

Jun 13,  · Algebraic \(K\)-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher \(K\)-groups and to.

Sep 05,  · The book, somewhat playfully titled The K-book, starts off in Weibel’s appealing no-nonsense style: “Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group Algebraic K-theory book a category and uses explicit algebraic presentations and higher algebraic K-theory which requires topological or homological.

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets. The K-Book: An Introduction to Algebraic K-theory (Graduate Studies in Mathematics) by Charles A.

Weibel | Jun 18, Hardcover $ $ Get it as soon as Fri, Aug 2. FREE Shipping by Amazon. Only 4 left in stock (more on the way). More Buying Choices $ (14 used. 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 menards.club: Hvedri Inassaridze. Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but 5/5(1).

American Mathematical Society · Charles Street Providence, Rhode Island · or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S.

Patent and Trademark Cited by: Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups.

These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained.

The equivariant algebraic K-theory is an algebraic K-theory associated to the category ⁡ of equivariant coherent sheaves on an algebraic scheme with action of a linear algebraic group, via Quillen's Q-construction; thus, by definition.

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0 ∧ or K1 ∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor.

From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis.

The results on K-theory are mostly of a veryAuthor: Richard G. Swan. Vector Bundles and K-Theory. This unfinished book is intended to be a fairly short introduction to topological K-theory, starting with the necessary background material on vector bundles and including also basic material on characteristic classes.

For further information or to download the part of the book that is written, go to the download page. Jun 24,  · Algebraic K-Theory and Its Applications book. Read reviews from world’s largest community for readers. Algebraic K-Theory plays an important role in many /5(2).

Algebraic K-theory is far more difficult and harder to define. For algebraic K-Theory by Milnor I have seen that the K-Groups are given by Milnor does what is now called "Milnor K-theory of fields" in his book, with an appendix explaining the relation (due to Tate) of $K_2$.

Algebraic K — Theory Proceedings of a Conference Held at Oberwolfach, June Part II. Editors: On the cohomology of SLn over rings of algebraic functions. Algebraic K — Theory Book Subtitle Proceedings of a Conference Held at Oberwolfach, June Part II.

I'm looking for a big-picture treatment of algebraic K-theory and why it's important. I've seen various abstract definitions (Quillen's plus and Q constructions, some spectral constructions like Waldhausen's) and a lot of work devoted to calculation in special cases, e.g., extracting information about K-theory from Hochschild and cyclic homology.

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability.

This book, based on a course at the University of Maryland in the fall ofis intended to enable graduate. Mar 02,  · Algebraic K-theory describes a branch of algebra that centers about two functors.

K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or. An exposition of K-theory and cyclic cohomology. It begins with examples of various situations in which the K-functor of Grothendieck appears naturally, including the topological and algebraic K-theory, K-theory of C*-algebras, and K-homology.

( views) The K-book: An introduction to algebraic K-theory by Charles Weibel - Rutgers, Lectures on K theory (PDF 95P) This lecture note covers the following topics: beginning of K theory, K theory of Banach algebras, Applications of topological Ktheory, The Atiyah- Singer index theorem, Algebraic K theory of Bass and Milnor applications, Higher Algebraic K theory, Hermitian K theory, Cyclic homology and K theory.

Jan 01,  · This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory.4/5(1). Book Description: This book contains accounts of talks held at a symposium in honor of John C.

Moore in October at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.

AT-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem (cf. Borel and Serre [2]). For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties.

Atiyah and Hirzebruch [3] con sidered a topological analog defined for any compact space X, a group K{X 5/5(2). Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations.

Thus, this. Algebraic K-Theory and Its Applications - Ebook written by Jonathan Rosenberg. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Algebraic K-Theory and Its menards.club: Jonathan Rosenberg.

In algebraic K-theory, the K-theory of a category C (usually equipped with some kind of additional data) is a sequence of abelian groups K i (C) associated to menards.club C is an abelian category, there is no need for extra data, but in general it only makes sense to speak of K-theory after specifying on C a structure of an exact category, or of a Waldhausen category, or of a dg-category, or.

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in menards.club: $ An Introduction to K-theory by Eric M.

Friedlander The author's objective was to provide participants of the Algebraic K-theory Summer School an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible with little or no prior knowledge of the subject.

In mathematics, topological K-theory is a branch of algebraic menards.club was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander menards.club early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch.

Quillen's "Higher Algebraic K-Theory I" is probably the best source for understanding the basics and the original intuition. Thomason/Trobaugh is also an excellent paper, but it is a fairly large paper and very fundamental (so the first half of the paper is dedicated to construction of the basic objects).Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory.

The broad range of these topics has tended to give the subject an aura of inapproachability.Get this from a library! Algebraic K-theory. [Victor P Snaith; Robert Wayne Thomason;] -- The conference proceedings volume is produced in connection with the second Great Lakes K-theory Conference that was held at The Fields Institute for Research in Mathematical Sciences in .