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.