Abstract
We study the formal properties of correspondences of curves without a core, focusing on the case of étale correspondences. The motivating examples come from Hecke correspondences of Shimura curves. Given a correspondence without a core, we construct an infinite graph together with a large group of “algebraic” automorphisms . The graph measures the “generic dynamics” of the correspondence. We construct specialization maps to the “physical dynamics” of the correspondence. Motivated by the abstract structure of the supersingular locus, we also prove results on the number of bounded étale orbits, in particular generalizing a recent theorem of Hallouin and Perret. We use a variety of techniques: Galois theory, the theory of groups acting on infinite graphs, and finite group schemes.
Citation
Raju Krishnamoorthy. "Correspondences without a core." Algebra Number Theory 12 (5) 1173 - 1214, 2018. https://doi.org/10.2140/ant.2018.12.1173
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