代数K理论及其应用Algebraic K-theory and its applications
- ISBN:9787510005145
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:23cm
- 页数:10,392页
- 出版时间:2010-02-01
- 条形码:9787510005145 ; 978-7-5100-0514-5
内容简介
Algebraic K-theory is the branch of algebra dealing with linear algebra (especially in the limiting case of large matrices) over a general ring R instead of over a field. It associates to any ring R a sequence of abelian groups Ki(R). The first two of these, K0 and K1, are easy to describe in concrete terms, the others are rather mysterious. For instance, a finitely generated projective R-module defines an element of K0(R), and an invertible matrix over R has a "determinant" in K1(R). The entire sequence of groups K1(R) behaves something like a homology theory for rings. Algebraic K-theory plays an important role in many areas, especially number theory, algebraic topology, and algebraic geometry. For instance, the class group of a number field is essentially K0(R), where R is the ring of integers, and "Whitehead torsion" in topology is essentially an element of K1(Zπ), where π is the fundamental group of the space being studied. K-theory in algebraic geometry is basic to Grothendieck's approach to the Riemann-Roch problem. Some formulas in operator theory, involving determinants and determinant pairings, are best understood in terms of algebraic K-theory. There is also substantial evidence that the higher K-groups of fields and of rings of integers are related to special values of L-functions and encode deep arithmetic information.
目录
作者简介
Jonathan Rosenberg ,美国马里兰大学帕克分校(University of Maryland, College Park)数学系教授。
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