Short course "Shimura varieties and interior motives". Lecture 1: Weight structures

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.