Deligne's proof in Weil I (Main lemma)

Abstract: After a quick review of $\ell$-adic local systems and the étale fundamental group, I will state and prove Deligne's "main lemma." I will then derive some consequences to be used in the next few talks, and if time permits, explain a key fact about $\operatorname{Sp}$-invariants used in the proof.

References:
$\bullet$ Milne, Lectures on Étale Cohomology, Section 30.
$\bullet$ Deligne, La Conjecture de Weil. I , Sections 1-3.
$\bullet$ Fulton and Harris, Representation Theory Appendix F.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.