Joint IAS/Princeton University Arithmetic Geometry Seminar

Motivic homotopy theory is a powerful framework for understanding algebraic varieties and the associated algebraic objects. Moreover, computations in the motivic stable homotopy category can also assist in the computation of stable homotopy groups of spheres.

In this talk, we will discuss the computation of motivic stable homotopy groups and their applications in classical computations. Specifically, we will discuss an example of complex motivic applications in classical theory, the Adams spectral sequence computations by Isaksen, Wang, and Xu. Their approach is based on a theoretical result by Gheorghe, Wang, and Xu about a t-structure on the p-complete cellular complex motivic category. We will explore a generalization of this result, which leads to computational applications in both classical and motivic Adams spectral sequences. This is joint work with Tom Bachmann, Guozhen Wang, and Zhouli Xu.