On the modularity of endomorphism algebras
Volume 71 / 2023
Bulletin Polish Acad. Sci. Math. 71 (2023), 23-33
MSC: Primary 11F41; Secondary 11F25, 11F70, 11F80, 14G32.
DOI: 10.4064/ba230310-29-3
Published online: 14 April 2023
Abstract
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 GL 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.
