The Riemann hypothesis for hypersurfaces

Abstract: I will talk about Katz' method of proving the Riemann hypothesis (RH) for hypersurfaces. The basic idea is very similar to what we saw last time: We reduce to showing RH for a particular hypersurface. Then we show RH for this particular hypersurface by a point-counting argument.

Reference: Katz, A note on Riemann hypothesis for curves and hypersurfaces over finite fields, Sections 5-8.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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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.

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