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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The relation between Quillen K-theory and Milnor K-theory in degree 4

## The relation between Quillen K-theory and Milnor K-theory in degree 4Add to your list(s) Download to your calendar using vCal - Oliver Roendigs (UniversitÃ¤t OsnabrÃ¼ck)
- Monday 13 June 2022, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory Besides the “canonical” homomorphism from Milnor K-theory to Quillen K-theory, Suslin constructed a Hurewicz homomorphism from Quillen K-theory to Milnor K-theory such that the resulting endomorphism on Milnor K-theory is multiplication with (n-1)! in degree n>0. Suslin’s conjecture, proven by himself in degree 3 as a consequence of joint work with Merkujev, says that the image of his Hurewicz homomorphism is as small as possible. Aravind Asok, Jean Fasel and Ben Williams proved Suslin’s conjecture in degree 5. My talk explains a proof of Suslin’s conjecture in degree 4 for fields of characteristic not dividing 6, based on their work and the computation of the one-line of motivic stable homotopy groups of spheres. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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