Applications of the large sieve to thin sets

Abstract: We review the proof of Cohen-Serre bound on the number of rational points on projective and affine varieties using the large sieve method and Lang-Weil bound on rational points on varieties over finite fields. Notice that stronger bounds are known now by work of Browning, Heath-Brown and Salberger.

algebraic geometrynumber theory

Audience: 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.