Global Fields

July 2 - 6, 2007, Moscow, Russia

Laboratoire J.-V. Poncelet

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Vasiliy Golyshev

Russia

Fano varieties and Galois representations

Given a deformation family of Fano varieties, one can construct certain Galois representations of global fields using mirror symmetry. Even those varieties that are motivically Tate (e.g. projective spaces or Grassmannians) yield non-trivial Galois representations. We describe some interesting instances of the construction, and explain how to compute Frobenius eigenvalues in these instances.