The most useful tool available have for computing homotopy groups is the Adams spectral sequence. Based on HFp, the E2-page takes a particularly nice form as Ext in the category of comodules over the dual Steenrod algebra. While this is great at computing stem by stem data, it is not so useful at extracting periodic data. On the other hand, the BP<n>-based Adams spectral sequence is better at isolating vn-periodicity, with the trade-off that its E1-page is much more delicate. At low heights, we are aided in this analysis by splitting results for BP<n>-cooperations.
This talk will investigate analogous questions in motivic homotopy theory. We will show that there are spectrum level splittings of the BPGL<0>- and BPGL<1>-cooperations algebras and how this translates to the corresponding Adams spectral sequences. Time permitting, we will discuss many potential avenues for future directions.