Viktor Burghardt (Northwestern): The Steenrod algebra of ​\widetilde{H\mathbb{Z}/l}

The Steenrod algebra of a cohomology theory is given by its stable operations. It acts on the cohomology ring of a given space and thus equips it with a module structure over the Steenrod algebra. This is additional data that imposes restrictions on what the cohomology ring of a space can be, and is thus helpful in practice. The Steenrod algebra of the motivic cohomology mod l spectrum \(H\mathbb{Z/l}\) has been computed by Voevodsky in the characteristic zero case. This computation has been extended to the essentially smooth over a field case away from the characteristic (i.e. to motivic cohomology mod l in \(SH(S)\) with \( l\neq \operatorname{char} S\) and S essentially smooth over a field) by Hoyois, Kelly and Østvær. The generalized motivic cohomology spectrum (aka the Milnor-Witt motivic cohomology spectrum) \(\widetilde{H\mathbb{Z}}\) is in some sense more natural to consider in motivic homotopy theory. In this talk we will take a look at its mod l Steenrod algebra.