Rigid local systems and motives of typeG2. With an appendix by Michale Dettweiler and Nicholas M. Katz

Abstract

AbstractUsing the middle convolution functorMCχintroduced by N. Katz, we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic groupG2. We derive the existence of motives for motivated cycles which have a motivic Galois group of typeG2. Granting Grothendieck’s standard conjectures, the existence of motives with motivic Galois group of typeG2can be deduced, giving a partial answer to a question of Serre.