Short course "Eisenstein Cohomology and Special Values of L-functions". Lecture 3: Motives and L-values

Short course 3/3, online talk.

One of the pillars of the Langlands program is a correspondence between motives and automorphic forms. On the motivic side, a celebrated conjecture of Deligne predicts the shape of rationality results for the critical values of motivic L-functions. Granting the Langlands correspondence, one may ask if Deligne's conjecture explains the results on critical values obtained (as in Lecture-2) by the techniques of Eisenstein cohomology. In the third talk, I will discuss the results of an ongoing project with Deligne on periods of motives and how they beautifully explain the results obtained on the automorphic side.