Modul:   MAT770  Oberseminar: Algebraische Geometrie

Rigid local systems

Vortrag von Dr. Michael Gröchenig

Sprecher eingeladen von: Prof. Dr. Joseph Ayoub

Datum: 16.10.17  Zeit: 13.15 - 14.45  Raum: Y27H25

An irreducible representation of an abstract group is called rigid, if it gives rise to 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 integrality. 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.