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

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dc.creatorYang, Lei
dc.date2006-12-14
dc.date.accessioned2026-07-07T07:34:51Z
dc.date.available2026-07-07T07:34:51Z
dc.descriptionIn 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.
dc.description89 pages
dc.identifierhttps://arxiv.org/abs/math/0612383
dc.identifierhttp://arxiv.org/abs/math/0612383
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119913
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11E76, 11F55, 11F80, 11G35, 11R39, 14G10, 14J32, 14J45
dc.titleGalois representations arising from twenty-seven lines on a cubic surface and the arithmetic associated with Hessian polyhedra
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