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- W2559968312 abstract "Algebraic K-theory is the meeting ground for various other subjects such as algebraic geometry, number theory, and algebraic topology. We will try to expose some of these connections. Due to the historical development of algebraic Ktheory, the field has two main components: the study of lower K-groups (in particular the Grothendieck group K0), which have explicit algebraic descriptions used in applications, and the study of higher K-theory, which requires much more sophisticated categorical and homotopical machinery. However, it is the more general categorical approach that allows for the means of proving the fundamental theorems that make K-theory into a field of study in its own right. We give a broad introduction to both lower and higher K-groups with a focus on Quillen’s “Q=Plus” theorem which proves that two different definitions of the K-groups, both very useful in different contexts, are the same: one definition uses the plus construction of the classifying space of the group GL(R) for a ring R, and the other uses Quillen’s Q-construction for an exact category. Then we present what is considered to be the most basic of the fundamental theorems in K-theory, the additivity theorem." @default.
- W2559968312 created "2016-12-16" @default.
- W2559968312 creator A5090563156 @default.
- W2559968312 date "2010-01-01" @default.
- W2559968312 modified "2023-09-23" @default.
- W2559968312 title "Topic Proposal Algebraic K-Theory and the Additivity Theorem" @default.
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