This is the continuation of Part 1 of the talk from a few weeks ago (the video of which is available on the seminar page). In the previous talk, after some motivation, I discussed a joint work with Kumar Murty on mixed motives with 3 weights and maximal unipotent radicals. In this sequel, I will fully generalize the picture to an arbitrary number of weights. In particular, I will discuss a generalization of Grothendieck’s theory of blended extensions for filtrations of an arbitrary finite length.

Background: Aside from assuming familiarity with the very basics of the theory of motives and tannakian formalism (namely, a basic familiarity with the philosophy of motives (say via realizations) and the definition of motivic Galois groups via tannakian formalism), the talk will be self-sufficient. The audience can watch the video of the first part of the talk for a brief review of this background material to the extent needed in this talk. (The interested audience might also benefit from watching the first part to learn more about the motivation and context.)