Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correspondences without a Core   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
$\mathcal{G}_{gen}\rightarrow\mathcal{G}_{phys}$ 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.

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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin