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I just came across Charles Weibel's Development of Algebraic K-Theory until 1980, and found it really helpful. Is there been anything analogous which surveys the developments in the last 30 years? I'd be particularly interested in understanding links (if they exist) to motivic theory, geometric Langlands and higher class field theory.

edited Jun 28 2011 at 18:41

David White
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asked Jun 28 2011 at 18:35

Jesse Wolfson
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Problably the most up-to-date survey is the Handbook of K-theory. – Fernando Muro Jun 28 2011 at 18:37

Fernando beat me by 43 seconds, probably because I went to find a link – David White Jun 28 2011 at 18:39

Hope you don't mind, I retagged your post to reflect the fact that it's asking for a book recommendation. – David White Jun 28 2011 at 18:40

Don't mind at all. I didn't realize there was a book that fit the bill :) – Jesse Wolfson Jun 28 2011 at 18:43

David White · Accepted Answer · 2011-06-28 18:38:23Z UTC

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I recommend the Handbook of K-theory. It was published in 2005 and Part II seems to contain what you're looking for.

answered Jun 28 2011 at 18:38

David White
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For the connections to motives, Bruno Kahn's paper in the Handbook is great. – Benjamin Antieau Jun 28 2011 at 19:08

Benjamin Antieau · Answer 2 · 2011-06-28 19:05:33Z UTC

I would suggest the lectures of Friedlander and Weibel: "An overview of algebraic K-theory" in Algebraic K-theory and its applications (Trieste 1997), 1999; MR. The later lectures include the modern point of view in terms of motivic cohomology and so forth together with connections to various theorems like the Milnor conjecture.

Survey of Algebraic K-Theory Since 1980?

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