The Bombieri-Stepanov approach to the Riemann hypothesis for curves over finite fields

30-Nov-2020, 20:00-21:30 (3 years ago)

Abstract: In this talk, we will discuss an elementary proof for the Riemann hypothesis for curves over finite fields due to Bombieri, based on previous work by Stepanov and Schmidt. It uses a method which we would now call the polynomial method, and the Riemann Roch theorem to prove an upper bound for the number of rational points on a curve.

algebraic geometrynumber theory

Audience: advanced learners

( paper | slides )

Comments: The slides for the talk will be available on Monday 30 November.


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.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

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.

Organizers: Raymond van Bommel*, Edgar Costa*, Bjorn Poonen*, Shiva Chidambaram*
*contact for this listing

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