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.
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3$\begingroup$ Problably the most up-to-date survey is the Handbook of K-theory. $\endgroup$– Fernando MuroCommented Jun 28, 2011 at 18:37
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$\begingroup$ Fernando beat me by 43 seconds, probably because I went to find a link $\endgroup$– David WhiteCommented Jun 28, 2011 at 18:39
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$\begingroup$ Hope you don't mind, I retagged your post to reflect the fact that it's asking for a book recommendation. $\endgroup$– David WhiteCommented Jun 28, 2011 at 18:40
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$\begingroup$ Don't mind at all. I didn't realize there was a book that fit the bill :) $\endgroup$– Jesse WolfsonCommented Jun 28, 2011 at 18:43
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2 Answers
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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
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$\begingroup$ For the connections to motives, Bruno Kahn's paper in the Handbook is great. $\endgroup$ Commented Jun 28, 2011 at 19:08
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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.
answered Jun 28, 2011 at 19:05