Computing and understanding stable homotopy groups of spheres is a fundamental problem in topology. Two classical methods are the Adams and Adams-Novikov spectral sequences. In this talk, I will discuss a new connection between the two spectral sequences through motivic homotopy theory over Spec C.

Motivic homotopy theory, introduced by Voevodsky and Morel, is a success applying homotopy theory to number theory and algebraic geometry. Our new connection is the other way around - we use motivic homotopy theory to extend computations of classical stable homotopy groups of spheres. The theoretic reason behind of the new connection is an equivalence of stable infinity categories in the sense of Lurie, between cellular motivic C/tau-modules and the derived category of BP_*BP-comodules.

This is a joint work with Bogdan Gheorghe, Dan Isaksen and Guozhen Wang.

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