Modul: MAT770 Oberseminar: Algebraische Geometrie

## Hermitian K-theory and algebraic cobordism of rings of integers and the slice spectral sequence

Dr. Jonas Kylling talk

Speaker invited by: Dr. Lorenzo Mantovani

**Date:** 03.06.19 **Time:** 13.15 - 14.45 **Room:** Y27H25

A powerful computational tool in topology is the Postnikov filtration, which gives rise to the Atiyah-Hirzebruch spectral sequence computing homotopy groups in terms of cohomology groups. In motivic homotopy theory there is a variant of this filtration known as the slice filtration, which gives a spectral sequence computing motivic homotopy groups in terms of motivic cohomology groups. We will carry out a computation of hermitian K-theory and algebraic cobordism of rings of integers using the slice filtration. As corollaries we get a variant of Milnor's conjecture on quadratic forms for rings of integers, and an analogy to the Lichtenbaum conjectures relating special values of zeta-functions to algebraic K-theory. This is based on joint work with Oliver Röndigs and Paul Arne Østvær.