Marco Schlichting
University of Warwick, UK
https://warwick.ac.uk/fac/sci/maths/people/staff/marco_schlichting/
On the relation of Milnor-Witt K-theory and Hermitian K-theory
Let R be a commutative local ring. There is a canonical multiplicative homomorphism KnWM(R) → GWnn(R) from Milnor-Witt K-theory of R to its Hermitian K-theory. I will explain recent improvements on homology stability of symplectic groups over local rings with infinite residue fields and use this to construct a map GWnn(R) → KnMWn(R) when n=2,3 mod 4. Finally, we compute the composition KnWM(R) → GWnn(R) → KnMWn(R). Using A1-homotopy theory, Asok, Fasel and Deglise have obtained similar results when R is in addition regular.
