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Endomorphisms of Jacobians of modular curves

โœ Scribed by Ernst Kani


Publisher
Springer
Year
2008
Tongue
English
Weight
217 KB
Volume
91
Category
Article
ISSN
0003-889X

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We confirm a conjecture of L. Merel (H. Darmon and L. Merel, J. Reine Angew. Math. 490 (1997), 81-100) describing a certain relation between the jacobians of various quotients of X p in terms of specific correspondences. The method of proof involves reducing this conjecture to a question about certa

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Very little is known about the existence of curves, and families of curves, whose Jacobians are acted on by large rings of endomorphisms. In this paper, we show the existence of curves X with an injection K / ร„ Hom(Jac(X ), Jac(X )) Z Q, where K is a subfield of even index at most 10 in a primitive