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

Subject: Mathematics

Class: Scientific


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.