Geometricity and Galois actions on fundamental groups

Speaker: 
Daniel Litt
Date: 
Fri, Jun 14, 2019
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Arithmetic Topology
Abstract: 
Which local systems on a Riemann surface X arise from geometry, i.e. as (subquotients of) monodromy representations on the cohomology of a family of varieties over X? For example, what are the possible level structures on Abelian schemes over X? We describe several new results on this topic which arise from an analysis of the outer Galois action on etale fundamental groups of varieties over finitely generated fields.