4 edition of **Algebraic K-theory and algebraic number theory** found in the catalog.

- 149 Want to read
- 19 Currently reading

Published
**1989**
by American Mathematical Society in Providence, R.I
.

Written in English

- K-theory -- Congresses.,
- Algebraic number theory -- Congresses.

**Edition Notes**

Statement | Michael R. Stein and R. Keith Dennis, editors. |

Series | Contemporary mathematics,, v. 83, Contemporary mathematics (American Mathematical Society) ;, v. 83. |

Contributions | Stein, Michael R., 1943-, Dennis, R. K. 1944- |

Classifications | |
---|---|

LC Classifications | QA612.33 .S46 1987 |

The Physical Object | |

Pagination | xiii, 488 p. ; |

Number of Pages | 488 |

ID Numbers | |

Open Library | OL2058920M |

ISBN 10 | 0821850903 |

LC Control Number | 88038151 |

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 : Hvedri Inassaridze. 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 Author: Hvedri Inassaridze.

Algebraic K-Theory by Olivier Isely - EPFL Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a field. Algebraic K-theory plays an important role in many subjects, especially number theory, algebraic topology and algebraic geometry. Get this from a library! Algebraic K-theory and algebraic number theory: proceedings of a seminar held January , , with support from the National Science Foundation and Japan Society for the Promotion of Science. [Michael R Stein; R K Dennis;].

Get this from a library! Applications of algebraic K-theory to algebraic geometry and number theory: proceedings of the AMS-IMS-SIAM joint summer research conference held June , , with support from the National Science Foundation. [Spencer Bloch; American Mathematical Society.; Institute of Mathematical Statistics.; Society for Industrial and Applied Mathematics.;]. Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a field. Algebraic K-theory plays an important role in many subjects, especially number theory, algebraic topology and algebraic geometry. In this document, I will briefly introduce the .

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In I wrote out a brief outline, following Quillen's paper Higher algebraic K-theory I. It was overwhelming. 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. 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: 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 Cited 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's Brand: Birkhäuser Basel. 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 s 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 Brand: Springer Netherlands. 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. 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. 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. I’ll try to add onto Kevin’s answer by talking about prerequisites to studying algebraic K-theory.

There are many different roads to algebraic K-theory, and this is part of what makes the subject so interesting: algebraic K-groups show up in algeb. wrote out a brief outline, following Quillen’s paper Higher algebraic K-theory I Q [].

It was overwhelming. I talked to Hy Bass, the author of the classic book Algebraic K-theory Bass [15], about what would be involved in writing such a book. It was scary, because (in ) I. I suggest looking at the introduction to Waldhausen's original paper on algebraic K-theory (Algebraic K-theory of generalized free products, Part I, Ann.

Math., () ). Waldhausen started out as a 3-manifold theorist, and he realized that certain phenomena in the topology of 3-manifolds would be explained if the Whitehead groups of. 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 Applications. 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.

Algebraic K-theory is a tool from homological algebra that defines a sequence of functors from rings to abelian groups. It has many applications in algebraic geometry. See also (topological-k-theory). 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 5/5(1).

Some K-theory of C*-algebras books also mention a little topological K-theory as a background, you can see this book: Blackadar B. K-theory for operator algebras[M]. Cambridge University Press, I am making some videos of K-theory(from topological to operator) in my language Chinese, if you can read Chinese or have some friend help to.

The Seminar on Algebraic K-theory and Algebraic Number Theory was held at the East- West Center in Honolulu, Hawaii on Januarywith support from the National Science Foundation, Grant DMS and the Japan Society for the Promotion of Science (JSPS).File Size: 1MB.

Dominique Arlettaz, Algebraic K-theory of rings from a topological viewpoint. Daniel Grayson, Quillen’s work in algebraic K-theory, J. K-Theory 11 (), – pdf. An introductory textbook account is in. Charles Weibel, The K-Book: An introduction to algebraic K-theory ; Further review includes.

The local structure of algebraic K theory. This note explains the following topics: Algebraic K-theory, Gamma-spaces and S-algebra, Reductions, Topological Hochschild homology, The trace K, Topological Cyclic homology, The comparison of K-theory and TC, Homotopical foundations.

Author(s): Bjorn Ian Dundas, Thomas G. Goodwillie and Randy McCarthy. An Introduction to Algebraic Number Theory. This note covers the following topics: Algebraic numbers and algebraic integers, Ideals, Ramification theory, Ideal class group and units, p-adic numbers, Valuations, p-adic fields.

Author(s): Frederique Oggier. What is algebraic number theory? A number ﬁeld K is a ﬁnite algebraic extension of the rational numbers Q.

Every such extension can be represented as all polynomials in an algebraic number α: K = Q(α) = (Xm n=0 anα n: a n ∈ Q). Here α is a root of a polynomial with coeﬃcients in Size: KB.Book Description: Algebraic K-theory describes a branch of algebra that centers about two functors.

K 0 and K 1, which assign to each associative ring ∧ an abelian group K 0 ∧ or K 1 ∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K 2, also from associative rings to abelian as functors K 0 and K 1 are important to.in order to solve some difficult problems in Algebraic Geometry (the letter “K” comes from the German word “Klassen”, the mother tongue of Grothendieck).

This idea of K-theory has invaded other parts of Mathematics, for example Number Theory [Ga], Topology [Bott] (AH1] and Functional Analysis [Connes]. Among many successes of K-theory.