Anandam Banerjee (IISER, Mohali) : Cycle class maps in the motivic stable homotopy category

Bloch constructed higher cycle class maps from higher Chow groups to Deligne cohomology and étale cohomology. I will define a map from the motivic Eilenberg-Mac Lane spectrum to the spectrum representing Deligne cohomology in the motivic stable homotopy category over C such that it gives Bloch's higher cycle class map on cohomology. The map is induced by the map from Voevodsky's algebraic cobordism spectrum MGL to the Hodge-filtered complex cobordism spectrum defined by Hopkins-Quick. This extends a result of Totaro showing that the usual cycle class map to singular cohomology factors through complex cobordism modulo the coefficients of the Lazard ring MU^{2*} tensor_L Z. This is joint work with Amit Hogadi.