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arXiv · 1705.08225

On the modularity of endomorphism algebras

François Brunault
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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 $\mathrm{GL}_2$ 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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François Brunault. 2017-06-29. On the modularity of endomorphism algebras. https://arxiv.org/abs/1705.08225

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