Lefschetz trace formula and proof of rationality and functional equation

Abstract: State the Lefschetz trace formula for étale cohomology, and explain how to apply it to the Frobenius morphism to deduce the Weil conjectures, excluding the Riemann hypothesis.

Reference: Milne, Lectures on étale cohomology, Section 25 and 27.

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.