Recognizing Galois representations of K3 surfaces View Full Text


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Article Info

DATE

2019-03

AUTHORS

Christian Klevdal

ABSTRACT

Under the assumption of the Hodge, Tate and Fontaine–Mazur conjectures we give a criterion for a compatible system of ℓ-adic representations of the absolute Galois group of a number field to be isomorphic to the second cohomology of a K3 surface. This is achieved by producing a motive M realizing the compatible system, using a local to global argument for quadratic forms to produce a K3 lattice in the Betti realization of M and then applying surjectivity of the period map for K3 surfaces to obtain a complex K3 surface. Finally we use a very general descent argument to show that the complex K3 surface admits a model over a number field. More... »

PAGES

16

References to SciGraph publications

  • 1992-12. Motives, numerical equivalence, and semi-simplicity in INVENTIONES MATHEMATICAE
  • 1993-12. Projective varieties with non-residually finite fundamental group in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s40993-019-0154-1

    DOI

    http://dx.doi.org/10.1007/s40993-019-0154-1

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