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- 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.
en.wikipedia.org/wiki/Algebraic_K-theory The story starts within algebraic geometry, when in 1957 Grothendieck de-ned K0 of an algebraic variety (which we now call the Grothendieck group of a variety) in order to prove a generalization of the Riemann-Roch theorem. It was de ned as follows: De nition 1.1.
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``The K-book: an introduction to algebraic K-theory'' - Rutgers …
``The K-book: an introduction to algebraic K-theory'' by Charles Weibel (Graduate Studies in Math. vol. 145, AMS, 2013) Errata to the published version of the K-book .
Introduction Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K0 of a category and uses explicit algebraic presentations, and higher …
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- This book is 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 classical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in...
This note is divided into four parts : Classical K-theory, Quillen’s higher K-theory, K-theory of brave new rings, and a short appendix collecting the few notions of homotopy theory used in …
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1.1 What is K-theory? 1.1.1 Roughly speaking, K-theory is the study of functors (bridges) C nC n K Kn: (Nice categories) (category of Abelian groups → → ∈Z (See 2.4 (ii) for a formal definition …
The $K$-book: An Introduction to Algebraic $K$-theory
This book is a comprehensive introduction to the subject of algebraic \(K\)-theory. It blends classical algebraic techniques for \(K_0\) and \(K_1\) with newer topological techniques for higher \(K\)-theory such as homotopy theory, …
An Algebraic Introduction to K-Theory - Cambridge …
Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields.
Introduction to Algebraic K-Theory - Princeton …
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 …
An Algebraic Introduction to K-Theory (Encyclopedia of …
Feb 4, 2010 · The reader will not only learn algebraic K-theory, but also Dedekind domains, class groups, semisimple rings, character theory, quadratic forms, tensor products, localization, …
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The K-book : an introduction to algebraic K-theory / Charles A. Weibel. pages cm. — (Graduate studies in mathematics ; volume 145) Includes bibliographical references and index.
The K-Book: An Introduction to Algebraic K-theory (Graduate …
Jan 1, 2013 · Algebraic K-theory is a field of abstract algebra concerning projective modules over a ring and vector bundles over schemes. It has many applications in mathematics such as …
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Introduction to Algebraic K-Theory - De Gruyter
Mar 2, 2016 · 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∧ …
There are three basic versions of the Grothendieck group K0. One involves the group completion construction, and is used for projective modules over rings, vector bundles over compact …
Algebraic K-theory - Wikipedia
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 …
K-theory - Wikipedia
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.In algebraic topology, it is a cohomology theory known as …
ALGEBRAIC K-THEORY BERTRAND GUILLOU 1. Introduction The idea will be to associate to a ring R a set of algebraic invariants, Ki(R), called the K-groups of R. We can even do a little …
Introduction to Algebraic K-Theory (Annals of Mathematics …
Jan 21, 1972 · 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∧ …
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- Author: John Milnor
Introduction to Algebraic K-Theory. (AM-72) on JSTOR
Algebraic K-theory describes a branch of algebra that centers about two functors. K0and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ ...
The K-book: An Introduction to Algebraic K-theory
The book is subdivided into six beefy chapters, with Grothendieck’s \(K_0\) apearing in Chapter II, with \(K_1\) and \(K_2\) (of a ring) appearing in Chapter III, and with the other middle chapters …
Introduction to Algebraic K-theory - Google Books
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...
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