Rigid G₂-representations and motives of type G₂

Titelangaben

Dettweiler, Michael ; Schmidt, Johannes:
Rigid G₂-representations and motives of type G₂.
In: Israel Journal of Mathematics. Bd. 212 (2016) Heft 1 . - S. 81-106.
ISSN 1565-8511
DOI: https://doi.org/10.1007/s11856-016-1295-8

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Abstract

We consider a family of motives associated to the rigid local system whose monodromy is dense in the simple algebraic group of type G2 and which has a local monodromy of order 7 at ∞. We prove an explicit Hilbert irreduciblity theorem for the associated étale realizations and deduce that the specialized motives at the points of irreducibility have motivic Galois group G2.