Abstracts for Conference on "Motives and Automorphic Forms" in Honour of Günter Harder's 85th Birthday

Short course 1/3.
Keywords: weight structures, weight filtrations, orthogonality, heart, weight filtrations avoiding certain weights.

We shall give a complete review of the abstract theory of (bounded) weight structures on triangulated categories, as developed by Bondarko. Using material from Levine's series "Three Lectures on Motivic cohomology", we shall see that Voevodsky's category of motives underlies a (unique) weight structure whose heart equals the additive category of Chow motives.

I will introduce the tantalizing problem of giving an automorphic interpretation of Bloch’s Tamagawa number reformulation of Birch-Swinnerton-Dyer, together with some results for the special case of Mordell-Weil rank r=1.

Short course 1/3, online talk,

In this introductory lecture, I will start by setting up the context to study the cohomology of a locally symmetric space. Then I will discuss the notions of inner, cuspidal, and Eisenstein cohomology, and their mutual relationships. Whereas to a large extent I will work with a general connected reductive group over a number field, I will often specialize to GL(n) over a totally real or a totally imaginary number field.

Short course 2/3.
Keywords: motivic weight structure, boundary motive, interior motive, semi-primality, minimal weight filtrations, weight conservativity.

After giving some motivation of the problem (applications to L-functions), we shall apply the theory presented in Lecture 1. This will culminate in a criterion concerning the existence of the interior motive. The criterion is formulated in "non-motivic" terms, i.e., it uses only (l-adic or Hodge theoretic) realisations.