Algebraic Topology Seminar

Over a field k, the zeroth homotopy group of the motivic sphere spectrum is given by the Grothendieck-Witt ring of symmetric bilinear forms GW(k). The Grothendieck-Witt ring GW(k) modulo the hyperbolic plane is isomorphic to the Witt ring of symmetric bilinear forms W(k) which further surjectively maps to Z/2. We may take motivic Eilenberg-Maclane spectra of Z/2. W(k) and GW(k). Voevodsky has computed the motivic Steenrod algebra of HZ/2 and solved the Bloch-Kato conjecture with its help. We go one step further and study the motivic Eilenberg-Maclane spectrum corresponding to the Witt ring and compute its dual Steenrod algebra. Speaker(s): Viktor Burghardt (Northwestern University)