Short course "Shimura varieties and interior motives". Lecture 2: Chow motives realising to interior cohomology of Shimura varieties

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.