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 Lazard ring MU*(-) ⊗L ℤ.
This is joint work with Amit Hogadi.
Published Sep. 27, 2017 11:44 AM
- Last modified Sep. 27, 2017 11:44 AM