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The relation between Quillen K-theory and Milnor K-theory in degree 4

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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.

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