Hana Jia Kang: Motivic Chow t-structure & computational tools for the R-motivic homotopy groups

I will first talk about the joint work with Tom Bachmann, Guozhen Wang and Zhouli Xu on motivic Chow t-structure. This t-structure is a generalization of the Chow-Novikov t-structure defined on a p-completed cellular motivic module category in work of Gheorghe--Wang—Xu. We identify the heart of this t-structure, and expand the results of Gheorghe—Wang--Xu to integral results on the entire motivic category over general base fields. It connects to the equivariant theory when field extensions are involved.

The Chow t-structure story leads to computational applications in determining the Adams spectral sequence differentials. Another useful computational tool is the effective spectral sequence. Work by Röndigs—Spitzweck—Østvær computes the 1-line of the motivic sphere over base fields of characteristic not two. In the on-going work with Eva Belmont and Dan Isaksen, we use the effective spectral sequence method and compute motivic homotopy groups over real numbers in a larger range.