Content of the course this semester

Hello, 

This semester is about Weil's Riemann hypothesis and a generalisation. Rough content: 

Part 1: Preliminaries (differential forms, cohomology groups in compact Kahler manifolds, Lefschetz fixed point theory)

Part 2: Serre's theorem on polarised morphisms of compact Kahler manifolds, Generalisation to meromorphic maps, Dynamical degrees

Part 3: Weil's Riemann hypothesis (=Deligne's theorem), Briefs on etale cohomology

Part 4: Some applications to number theory (exponential sums, Ramanujan-Peterson conjecture)

Part 5: Intersection of algebraic cycles, Chow's moving lemma, Dynamical degrees in non-zero characteristic

Part 6: A generalisation of Weil's Riemann hypothesis, Evidence, Recent work

Part 7: The standard conjecture, Application to the conjecture in Part 6

References will be provided later.