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On the modularity of endomorphism algebras

Brunault François

Bulletin of the Polish Academy of Sciences. Mathematics

2023

Vol. 71, no 1

22--33

We show that any homomorphism between Jacobians of modular curves arises from a linear combination of Hecke modular correspondences. The proof uses the adelic language and 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.