Integrality of the Betti Moduli Space

Explore a detailed lecture on the integrality of the Betti moduli space, presented by Johan de Jong from Columbia University at the Institut des Hautes Etudes Scientifiques (IHES). Delve into joint research with Hélène Esnault, examining the properties of moduli spaces of irreducible representations of topological fundamental groups for smooth projective varieties over complex numbers. Investigate the concept of purity over the spectrum of integers and its implications for the structure of these moduli spaces. Learn about weak answers to key questions in this field and their applications in excluding certain abstract groups as fundamental groups of smooth projective varieties. Gain insights into the methodology used for studying these phenomena and its potential for further research in algebraic geometry and topology.