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Galois action on $\bar{\mathbb Q}$-isogeny classes of abelian $L$-surfaces with quaternionic multiplication

Volume 181 / 2017

Santiago Molina Acta Arithmetica 181 (2017), 369-392 MSC: Primary 11G18; Secondary 11G10. DOI: 10.4064/aa170504-20-9 Published online: 8 December 2017

Abstract

We construct a projective Galois representation attached to an abelian $L$-surface with quaternionic multiplication, describing the Galois action on its Tate module. We prove that such a representation characterizes the Galois action on the isogeny class of the abelian $L$-surface, seen as a set of points of a certain Shimura curve.

Authors

  • Santiago MolinaCentre de Recerca Matemática CRM
    08176 Bellaterra, Barcelona, Spain
    e-mail

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