Speaker: Michael Dettweiler (Heidelberg Univ.)
Title: Motives with Galois group G_2

Abstract : Abstract: Motives can be seen as universally defined subspaces of the cohomology of varieties. The Langlands Program links the theory of motives with the theory of modular forms. In the Proceedings of the 1991-Seattle conference on motives, Serre asks the "very hazardeous" question:

Do there exist motives with Galois group isomorphic to the simple algebraic group G_2 (or E_8)?

Hodge theory implies that such motives of type G_2 and E_8 cannot occur in the (untwisted) cohomology of Shimura varieties - which makes them hard to construct. Using the middle convolution and previous work of Feit, Fong and Thompson, we (Stefan Reiter and myself) construct G_2-motives explicitly, giving a positive answer to Serre's question in the G_2-case.