Remy van Dobben de Bruyn (MPI for Mathematics, Bonn): A condensed proof of the étale and pro-étale exodromy correspondences

Abstract: The category of locally constant étale sheaves on a scheme is controlled by the étale fundamental group, via the monodromy correspondence. Following ideas of MacPherson, this was upgraded to an “exodromy correspondence” for constructible étale sheaves by Barwick, Glasman, and Haine in 2018. While the statement is purely algebro-geometric, their proof ventures deep into higher topos theory. I will present a direct geometric proof via condensed mathematics.