Rigid local systems
Michael Groechenig (Freie Universität Berlin)
Wednesday 15th November, 2017 15:00-16:00 Maths 311B
An irreducible representation of an abstract group is called rigid, if it defines an isolated point in the moduli space of all representations. Complex rigid representations are always defined over a number field. According to a conjecture by Simpson, for fundamental groups of smooth projective varieties one should expect furthermore that rigid representations can be defined over the ring of algebraic integers. I will report on joint work with H. Esnault where we prove this for so-called cohomologically rigid representations. Our argument is mostly arithmetic and passes through fields of positive characteristic and the p-adic numbers.