Informally, $K$-theory is a tool for probing the structure of a
mathematical object such as a ring or a topological space in terms
of suitably parameterized vector spaces and producing important
intrinsic invariants which are useful in the study of algebraic and
geometric questions. 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 computations. The
resulting interplay of algebra, geometry, and topology in
$K$-theory provides a fascinating glimpse of the unity of
mathematics. 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, spectra, and
cohomological descent. The book takes the reader from the basics of
the subject to the state of the art, including the calculation of
the higher $K$-theory of number fields and the relation to the
Riemann zeta function.
General
| Imprint: |
American Mathematical Society
|
| Country of origin: |
United States |
| Series: |
Graduate Studies in Mathematics |
| Release date: |
July 2013 |
| Authors: |
Charles A. Weibel
|
| Dimensions: |
260 x 182 x 40mm (L x W x T) |
| Format: |
Hardcover
|
| Pages: |
618 |
| ISBN-13: |
978-0-8218-9132-2 |
| Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
| LSN: |
0-8218-9132-4 |
| Barcode: |
9780821891322 |
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