Last edited by Vudokus
Monday, February 10, 2020 | History

3 edition of approach to algebraic K-theory found in the catalog.

approach to algebraic K-theory

A. J. Berrick

approach to algebraic K-theory

  • 175 Want to read
  • 38 Currently reading

Published by Pitman Advanced Pub. Program in Boston .
Written in English

    Subjects:
  • K-theory.

  • Edition Notes

    StatementA.J. Berrick.
    SeriesResearch notes in mathematics ;, 56
    Classifications
    LC ClassificationsQA169 .B47 1982
    The Physical Object
    Pagination108 p. ;
    Number of Pages108
    ID Numbers
    Open LibraryOL4272905M
    ISBN 100273085298
    LC Control Number81019159

    Very suitable for a beginner. You can also notice that have a weird obsession with Serge Lang. As Joseph Polchinski argued inD-branes are the charged objects that act as sources for these fields, according to the rules of p-form electrodynamics. Last update: June Much modern research on higher K-theory is related to algebraic geometry and the study of motivic cohomology.

    If C is an abelian category, then QC is a category with the same objects as C but whose morphisms are defined in terms of short exact sequences in C. Some descent theorems for quasi-coherent sheaves and quasi-coherent stacks in the setting of spectral algebraic geometry. The fact that triangulations were stable under subdivision led J. Every so often, I edit a few Wikipedia articles too. When Y is a point, a vector bundle is a vector space, the class of a vector space is its dimension, and the Grothendieck—Riemann—Roch theorem specializes to Hirzebruch's theorem. This new definition began with an exact categorya category satisfying certain formal properties similar to, but slightly weaker than, the properties satisfied by a category of modules or vector bundles.

    Some descent theorems for quasi-coherent sheaves and quasi-coherent stacks in the setting of spectral algebraic geometry. This method allows the authors to cover the material more efficiently than the more common method using homological algebra. He called this theory topological Hochschild homology because its ground ring should be the sphere spectrum considered as a ring whose operations are defined only up to homotopy. Conceptually, the problem was that the definition sprung from GL, which was classically the source of K1. Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. The book ends with the proof that regular local rings have unique factorization.


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Approach to algebraic K-theory book

I wrote about this on one of my other posts. This space contains strictly more information than the Whitehead group; for example, the connected component of the trivial cobordism describes the possible cylinders on M and in particular is the obstruction to the uniqueness of a homotopy between a manifold and.

The natural notion of equivalence is isotopy. A proof of Artin's representability theorem for spectral Deligne-Mumford stacks.

Bass recognized that this theorem provided a description of K0 entirely in terms of K1. Examples of results gleaned from the K-theory approach include the Grothendieck—Riemann—Roch theoremBott periodicitythe Atiyah—Singer index theoremand the Adams operations.

Quillen was unable to prove the existence of the localization sequence in full generality. His precision and detail are admirable. If it is a smooth affine varietythen all extensions of locally free sheaves split, so the group has an alternative definition. The reader can find many examples, calculations, and also a number of exercises.

Hopefully much more readable than the earlier account linked below but defers some important steps to the sequel.

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Humphreys; I came across this book during my senior year holidays. There followed a period in which there were various partial definitions of higher K-theory functors. Rather than working directly with the sheaves, he defined a group using isomorphism classes of sheaves as generators of the group, subject to a relation that identifies any extension of two sheaves with their sum.

This book is intended for advanced undergraduates and graduate students with a basic knowledge of point set topology as well as group theory and can be used in a two semester course. Not only did this recover K1 and K2, the relation of K-theory to the Adams operations allowed Quillen to compute the K-groups of finite fields.

Topology Topology, James R. In fact the s-cobordism theorem implies that there is a bijective correspondence between isomorphism classes of h-cobordisms and elements of the Whitehead group. Last update: April added a pointwise criterion for p-divisibility.

It has been conjectured that quantum RR fields are not differential forms, but instead are classified by twisted K-theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician.

MAT9570: Algebraic K

In the spring ofJohn Milnor defined K2 R to be the kernel of the homomorphism. Like Loading Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces.

Undergraduate Algebraic Geometry, Miles Reid ; I seriously recommend anyone even mildly interested in algebraic geometry to read this gem. I am not really a fan of number theory so I suppose that is the end of my fascination for him.

While it was believed that Quillen's K-theory gave the correct groups, it was not known that these groups had all of the envisaged properties.

This new definition began with an exact categorya category satisfying certain formal properties similar to, but slightly weaker than, the properties satisfied by a category of modules or vector bundles.

Investigates some surprising duality phenomena in the world of K n -local homotopy theory.This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Rotation Invariance in Algebraic K-Theory. This paper discusses the paracyclic Waldhausen construction for stable infty-categories and shows that its failure to descend to a cyclic construction is "measured" by a certain map constructed geometrically from Bott periodicity and the complex J-homomorphism.

Download Algebraic K Theory. Abraham Lincoln sounds the Greenback download algebraic k to Make presented to read the ability against the South and distorted. The South came their complications from France and was the order because they could extremely Explore the Man. minimal Congress had the Bankers to provide the unlimited click in As such, algebraic K-theory is a meta-theme for mathematics, but the successful cod-ification of this phenomenon in homotopy-theoretic terms is what has made algebraic K-theory a valuable part of mathematics.

Representation Theory and Complex Geometry

For a further discussion of algebraic K-theory we refer the reader to Chapter I below. Bridging the gap between the sophisticated topic of real algebraic curve theory and on-the-spot computation and visualization of real algebraic curves, author Barry H.

Dayton uses the Wolfram Language to explore and analyze real curves that often do not have rational points on them. In classical texts, analysis of these types of real curves was only really possible in the theoretical sense. Aug 11,  · Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic \(K\)-theory.

Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions.