Time：16:00-17:30, Friday, September 18 2026
Venue：E14-116
Speaker：Marc Hindry，Institut de Mathématiques de Jussieu‑Paris Rive Gauche
Title：Arithmetic of algebraic surfaces over finite fields
Abstract：Classical algebraic geometry studies varieties defined over the complex field, the analogous geometry over finite fields enjoys both similar and different aspects. We will discuss how to measure the complexity of the geometry of an algebraic surfaces (for example, how do curves intersect on it?). A good quantity to estimate this complexity is the discriminant of the intersection pairing on the group of curves modulo deformations (the so-called Néron-Severi group). In general, for example when working over the complex numbers, we have very few tools to estimate this discriminant. In the very interesting case of surfaces over a finite field, we will show that ideas coming from number theory (special values of zeta functions, etc.) lead to interesting results. The talk will be accessible to all mathematicians.
