On the modularity of endomorphism algebras

2017/05/23 by Brunault, François
#11F25 #11F41 (Primary) #11F70 #11F80 #14G32 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1705.08225

Abstract

We use the adelic language to show that any homomorphism between Jacobians of modular curves arises from a linear combination of Hecke modular correspondences. The proof is based on a study of the actions of GL₂ and Galois on the étale cohomology of the tower of modular curves. We also make this result explicit for Ribet's twisting operators on modular abelian varieties.

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