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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119913In 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 Lie algebra $E_6$. We give a conjecture about the identification of two different kinds of $L$-functions which can be considered as a higher dimensional counterpart of the Langlands-Tunnell theorem.89 pagesNumber TheoryAlgebraic Geometry11E76, 11F55, 11F80, 11G35, 11R39, 14G10, 14J32, 14J45Galois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedratext