2008/05/29 by Ángel Carocca, A. Carocca, Carocca, A. +9 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #math.AG #msc:14H40 #msc:14K10
paper · pdf · doi:10.48550/arxiv.0805.4563
24 pages. Accepted in J. Reine Angew. Math. Minor changes
arxiv created 2008/08/18 · arxiv updated 2009/12/01
Let G denote a finite group and π: Z → Y a Galois covering of smooth projective curves with Galois group G. For every subgroup H of G there is a canonical action of the corresponding Hecke algebra ℚ[H \backslash G/H] on the Jacobian of the curve X = Z/H. To each rational irreducible representation W of G we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve X and thus an abelian subvariety P of the Jacobian JX. We give sufficient conditions on W, H, and the action of G on Z, which imply P to be a Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of arbitrary exponent in this way.