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Friday, August 7, 2020 | History

5 edition of Algebraic K-Theory, Part 2 found in the catalog.

Algebraic K-Theory, Part 2

R. Keith Dennis

Algebraic K-Theory, Part 2

by R. Keith Dennis

  • 12 Want to read
  • 31 Currently reading

Published by Springer-Verlag .
Written in English


Edition Notes

SeriesLecture Notes in Mathematics, Vol 967
ID Numbers
Open LibraryOL7443148M
ISBN 100387119663
ISBN 109780387119663

For schemes. For schemes, there are two constructions which do not agree in full Thomason-Trobaugh Quillen K-theory. The Quillen K-theory of a scheme X X is defined as the algebraic K-theory of the exact category Vect (X) Vect(X) of vector bundles on X X (using the Quillen Q-construction).. Thomason-Trobaugh K-theory. Let Perf (X) Perf(X) be the category of perfect. A survey of surface braid groups and the lower algebraic K-theory of their group rings John Guaschi Normandie Université, UNICAEN, as well as some books and monographs [26,99,,], for the most part, the theory of surface braid groups is discussed in little detail in these works. The aim of this article is two-fold, the first being to.

Algebraic K-Theory and its Applications by Jonathan Rosenberg Errata to the Second Printing, I am quite grateful to those who have sent me their comments on this book. I especially thank Paul Arne Ostvaer, Ioannis Emmanouil, Desmond Sheiham, Efton Park, Jon Berrick, Henrik Holm, Mike Boyle, and Hanfeng Li for their corrections. Chapter I. Algebraic K-Theory Proceedings of a Conference Held at Oberwolfach, June Part I. Editors; R. Keith Dennis.

Applications of algebraic K-theory to algebraic geometry and number theory (part 2): proceedings. 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.


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Algebraic K-Theory, Part 2 by R. Keith Dennis Download PDF EPUB FB2

Buy Part 2 book K ― Theory: Proceedings of a Conference Held at Oberwolfach, June Part II (Lecture Notes in Mathematics) (English and French Edition) Format: Hardcover. In particular, the (higher) K-theory of a ring R is defined as the product of the group of units of the classifying space of R and K0(R).

The author shows that this definition of K-theory does coincide with that of K0 and K1 done earlier in the by: 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 by: ``The K-book: an introduction to algebraic K-theory'' by Charles Weibel (Graduate Studies in Math.

vol.AMS, ). Errata to the published version of the K-book. Algebraic K — Theory Proceedings of a Conference Held at Oberwolfach, June Part II. Editors: Dennis, R. Keith (Ed.) Free Preview. Algebraic K-Theory Unknown Binding – January 1, See all 2 formats and editions Hide other formats and editions.

Price New from Used from Hardcover "Please retry" — — $ Paperback "Please retry" $ Manufacturer: W. Benjamin. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are Part 2 book, S3 and S7.

Moreover, it is possible to derive a substantial part of stable homotopy theory from by:   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.

Handbook of K theory This two-volume handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a leading expert.

Publication: Graduate Studies in Mathematics Publication Year: ; Volume ISBNs: (print); (online). Applications of algebraic K-theory to algebraic geometry and number theory, Part 2 About this Title. Spencer J. Bloch, R. Keith Dennis, Eric M. Friedlander and Michael R. Stein, Editors. Publication: Contemporary Mathematics Publication Year Volume ISBNs: (print); (online).

An introduction to algebraic K Theory. This book covers the following topics: Projective Modules and Vector Bundles, The Grothendieck group K_0, K_1 and K_2 of a ring, higher K-theory, The Fundamental Theorems of higher K-theory and the higher K-theory of Fields.

Author(s): Charles Weibel. 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 veryBrand: Springer-Verlag Berlin Heidelberg. 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 : Birkhäuser Basel.

Chapter 1, containing basics about vector bundles. Part of Chapter 2, introducing K-theory, then proving Bott periodicity in the complex case and Adams' theorem on the Hopf invariant, with its famous applications to division algebras and parallelizability of spheres.

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.

K-theory is often considered a complicated mathematical theory for specialists only. This book is an accessible introduction to the basics and provides detailed explanations of the various concepts required for a deeper understanding of the subject.

Some familiarity with basic C*algebra theory is assumed. The book then follows a careful construction and analysis of the operator K-theory groups. Table of Contents: Part II viii 9 free Introduction xi 12 free List of Talks xiii 14 free List of Participants xv 16 free Letters from Browder to Dennis and Stein concerning the image of K3 (Z[ζp]) and K3 (Z) in K3 of a finite field 20 free A comparison theorem for the 2-rank of K2 (θ) 24 The Hilbert polynomial of a union of lines 34 A note on injectivity of lower K-groups for.

The algebraic K-theory presented here is, essentially, a part of general linear algebra. It is concerned with the structure theory of projective modules, and of their automorphism groups.

Thus, it is a generalization, in the most naive sense, off the theorem asserting the existence and uniqueness of bases for vector spaces, and of the group.

The K-Book: An Introduction to Algebraic K-Theory Charles A. Weibel Informally, K-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebraic and geometric questions.

This book deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools.

Many of the techniques extend to the general case. The last section of the book, § VI, is devoted to the K-theory of the ring of integers and includes a particularly beautiful result, modulo Vandiver’s Conjecture, having to do with the Picard group of a certain algebraic extension of \(\mathbb{Z}\) at a sum of two natural l-th roots of unity for an irregular prime l (to wit: the indicated.Abstract.

This chapter begins with a nontechnical overview of algebraic K-theory, including some historical motivation and its development.

This is followed by the introduction of Waldhausen’s S-construction and proofs of its essential first y, algebraic K-theory is compared with the homology of categories, providing a first model for the “differential” of algebraic K Cited by: 2.