Explicit description of boundary map in algebraic K-theory - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T05:37:18Z http://mathoverflow.net/feeds/question/61007 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61007/explicit-description-of-boundary-map-in-algebraic-k-theory Explicit description of boundary map in algebraic K-theory Dustin Clausen 2011-04-08T00:05:17Z 2011-04-08T01:33:16Z <p>Recall that for a DVR A with fraction field F and residue field k, there is a "localization" fiber sequence in algebraic K-theory,</p> <p>$$K(k) \rightarrow K(A) \rightarrow K(F).$$</p> <p>In Remark 5.17 of his "Higher Algebraic K-theory: I" paper, Quillen gives an explicit description of the corresponding boundary map $\partial:\Omega K(F) \rightarrow K(k)$, saying the proof will be in a later paper. My question is, has a proof appeared in the literature? I'd also be happy with proofs in the literature of any similar descriptions, e.g. involving the S-dot construction.</p> <p>Thank you for reading!</p>