# Seminario: Weil Conjectures and Moduli of Vector Bundles

## Martedì 23 Settembre, ore 14:30 - Aula 2AB45 - Frank Neumann

ARGOMENTI: Seminari

SEMINARIO

Martedì 23 Settembre alle ore 14:30 in aula 2AB45, Frank Neumann dell'Università di Leicester terrà un seminario dal titolo "Weil Conjectures and Moduli of Vector Bundles".

Abstract
In 1949, Weil conjectured deep connections between the topology, geometry and arithmetic of projective algebraic varieties over a field in characteristic p, including an analogue of the celebrated Riemann Hypothesis. These conjectures led to the development of etale cohomology in algebraic geometry as an analog of singular cohomology in algebraic topology by Grothendieck and his school and culminated in the proof of the Weil conjectures by Deligne in the 70s. After giving a gentle introduction into the classical Weil conjectures for projective algebraic varieties and discussing what moduli problems and moduli stacks are, I will outline how an analog of these Weil conjectures for the moduli stack of vector bundles over a projective algebraic curve can be formulated and proved. This basically comes down to counting how many vector bundles (up to isomorphisms) there are over a given algebraic curve in characteristic p.