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Rigid G 2-representations and motives of type G 2

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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 G 2 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 G 2.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bayreuth, Universitätsstr. 30, D-95447, Bayreuth, Germany

    Michael Dettweiler

  2. Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 288, D-69120, Heidelberg, Germany

    Johannes Schmidt

Authors
  1. Michael Dettweiler
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  2. Johannes Schmidt
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Corresponding author

Correspondence to Michael Dettweiler.

Additional information

The first author gratefully acknowledges financial support from the DFGHeisenberg Grant DE-1442.

The second author gratefully acknowledges financial support from the DFGForschergruppe 1920 “Symmetrie, Geometrie und Arithmetik”, Heidelberg–Darmstadt.

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Dettweiler, M., Schmidt, J. Rigid G 2-representations and motives of type G 2 . Isr. J. Math. 212, 81–106 (2016). https://doi.org/10.1007/s11856-016-1295-8

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  • DOI: https://doi.org/10.1007/s11856-016-1295-8

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