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

Algebraic K-Theory, Part 2

R. Keith Dennis

- 12 Want to read
- 31 Currently reading

Published
**May 1983**
by Springer-Verlag
.

Written in English

**Edition Notes**

Series | Lecture Notes in Mathematics, Vol 967 |

ID Numbers | |
---|---|

Open Library | OL7443148M |

ISBN 10 | 0387119663 |

ISBN 10 | 9780387119663 |

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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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.