Algebraic Geometry Seminar

For each (isogeny class of) simple exceptional algebraic group G, Serre asked if there exist motives with Galois group G. We now have a complete answer to this question, due to work of many authors: all exceptional groups do in fact appear. A stronger question is the function field analogue: does there exist a motivic local system with monodromy group G? In this case, the answer was known except in the case G has type E_6. I'll explain joint work with Krämer and Maculan constructing infinitely many essentially distinct motivic local systems with monodromy group E_6.