Using the middle convolution functor MCχ introduced by N.Katz, we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic group G2. We derive the existence of motives for motivated cycles which have a motivic Galois group of type G2. Granting Grothendiecks standard conjectures, the existence of motives with motivic Galois group of type G2 can be deduced, giving a partial answer to a question of Serre.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- local systems
- middle convolution