Adeel Khan (September 9, 2022): An invitation to motivic sheaves (part 1)
Channel: Algebraic Geometry at Stanford
Date: 2022-09-10

These lectures will be an introduction to Voevodsky's theory of motivic sheaves.  In the first lecture we will try to understand what the theory is supposed to look like, according to Beilinson's 1985 conjectures.  To better appreciate these we will briefly review some of the ideas that influenced him, such as Grothendieck's theory of pure motives and Deligne's theory of mixed Hodge structures (i.e., why motives?), and the six functor formalism on l-adic sheaves (i.e., why sheaves?).  In the second lecture, we will begin looking into Voevodsky's work on actually constructing categories of motivic sheaves, as well as the connection with invariants like Chow groups and algebraic K-theory.

Despite the seemingly forbidding nature of the topic, these lectures are intended for an audience with familiarity with basic algebraic geometry, but no familiarity with any of the advanced topics being addressed.