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- W3100682659 abstract "We study the formal properties of correspondences of curves without a core, focusing on the case of '{e}tale correspondences. The motivating examples come from Hecke correspondences of Shimura curves. Given a correspondence without a core, we construct an infinite graph $mathcal{G}_{gen}$ together with a large group of algebraic automorphisms $A$. The graph $mathcal{G}_{gen}$ measures the generic dynamics of the correspondence. We construct specialization maps $mathcal{G}_{gen}rightarrowmathcal{G}_{phys}$ to the physical dynamics of the correspondence. We also prove results on the number of bounded '{e}tale 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." @default.
- W3100682659 created "2020-11-23" @default.
- W3100682659 creator A5036572206 @default.
- W3100682659 date "2018-07-31" @default.
- W3100682659 modified "2023-09-23" @default.
- W3100682659 title "Correspondences without a core" @default.
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- W3100682659 doi "https://doi.org/10.2140/ant.2018.12.1173" @default.
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