A1 homotopy groups of GL_n and a problem of Suslin's

Ben Williams (University of British Columbia)

07-Dec-2020, 15:40-16:30 (3 years ago)

Abstract: Let $F$ be an infinite field. Andrei Suslin constructed a morphism from the (Quillen) K-theory of $F$ to the Milnor K-theory of $F$: $s_n : K_n(F) \to K_n^M(F)$. He proved that the image of $s_n$ contains $(n-1)! K_n^M(F)$. He raised the question of whether this accounted for the whole imageā€”it was known to when $n$ is $1$, $2$ or $3$. In this talk I will explain how one can partially recover this morphism as a morphism of $A^1$-homotopy groups of down-to-earth objects, and I will show how this tells us some things about Suslin's question when $n$ is $4$ and settles it when $n$ is $5$. This talk represents joint work with Aravind Asok and Jean Fasel.

algebraic topologycategory theorygroup theoryK-theory and homology

Audience: researchers in the topic

( video )


Cihan Okay

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Organizer: Cihan Okay*
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