most recent 30 from http://mathoverflow.net 2013-05-19T18:35:23Z http://mathoverflow.net/feeds/question/69044 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69044/survey-of-algebraic-k-theory-since-1980 Jesse Wolfson 2011-06-28T18:35:22Z 2011-06-28T19:05:33Z

<p>I just came across Charles Weibel's <a href="http://www.math.rutgers.edu/~weibel/papers-dir/khistory.pdf" rel="nofollow">Development of Algebraic K-Theory until 1980</a>, 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.</p>

http://mathoverflow.net/questions/69044/survey-of-algebraic-k-theory-since-1980/69045#69045 David White 2011-06-28T18:38:23Z 2011-06-28T18:38:23Z

<p>I recommend the <a href="http://www.math.uiuc.edu/K-theory/handbook/" rel="nofollow">Handbook of K-theory</a>. It was published in 2005 and Part II seems to contain what you're looking for.</p>

http://mathoverflow.net/questions/69044/survey-of-algebraic-k-theory-since-1980/69047#69047 Benjamin Antieau 2011-06-28T19:05:33Z 2011-06-28T19:05:33Z

<p>I would suggest the lectures of Friedlander and Weibel: "An overview of algebraic K-theory" in <em>Algebraic K-theory and its applications (Trieste 1997)</em>, 1999; <a href="http://www.ams.org/mathscinet/search/publdoc.html?arg3=&amp;co4=AND&amp;co5=AND&amp;co6=AND&amp;co7=AND&amp;dr=all&amp;pg4=AUCN&amp;pg5=TI&amp;pg6=CC&amp;pg7=ALLF&amp;pg8=ET&amp;r=1&amp;review_format=html&amp;s4=friedlander%2520and%2520weibel&amp;s5=&amp;s6=&amp;s7=&amp;s8=All&amp;vfpref=html&amp;yearRangeFirst=&amp;yearRangeSecond=&amp;yrop=eq" rel="nofollow">MR</a>. 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.</p>