Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedra

  title={Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedra},
  author={Lei Yang},
  journal={arXiv: Number Theory},
  • Lei Yang
  • Published 14 December 2006
  • Mathematics
  • arXiv: Number Theory
In the present paper, we will show that three apparently disjoint objects: Galois representations arising from twenty-seven lines on a cubic surface (number theory and arithmetic algebraic geometry), Picard modular forms (automorphic forms), rigid Calabi-Yau threefolds and their arithmetic (Diophantine geometry) are intimately related to Hessian polyhedra and their invariants. We construct a Galois representation whose image is a proper subgroup of $W(E_6)$, the Weyl group of the exceptional… 
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