Aleksander Shmakov: Towards mixed motivic L-functions and conjectures beyond Beilinson

Abstract:

The conjectures of Beilinson and Bloch–Kato are a vast generalization of the analytic class number formula and the conjectures of Birch and Swinnerton–Dyer, relating special values of L-functions attached to motives over number fields to period integrals and tthe regulator morphisms out of motivic cohomology or algebraic K-theory. I will explain a particularly efficient formulation of these conjectures due to Fontaine and Perrin–Riou, and then give some sample of examples and phenomena involving mixed motivic periods which fall outside these conjectures, but which fit into a more expansive story involving some larger class of mixed motivic L-functions.