I will talk about joint work with Tom Bachmann, Guozhen Wang and Zhouli Xu on the Chow t-structure on the motivic stable homotopy category over a general base field. We identify the heart of this t-structure and show the algebraicity of a certain motivic module category. Our work generalizes the work of Gheorghe--Wang--Xu; it leads to computational applications in the classical and motivic Adams spectral sequences. 

Time permitting, I will also talk about the motivic slice computation of the motivic 'image-of-j' spectrum defined by Bachmann--Hopkins. The comparison between the motivic slice spectral sequence and the motivic Adams spectral sequence parallels the classical Adams and Adams--Novikov spectral sequences. The slice computation is joint with Eva Belmont and Dan Isaksen.

1.14.pdf