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Dettaglio pubblicazione

2022, ALGEBRA & NUMBER THEORY, Pages 1423-1461 (volume: 16)

Automorphisms of Cartan modular curves of prime and composite level (01a Articolo in rivista)

Dose Valerio, Lido GUIDO MARIA, Mercuri Pietro

We study the automorphisms of modular curves associated to Cartan subgroups of GL(2,Z/nZ) and certain subgroups of their normalizers. We prove that if n is large enough, all the automorphisms are induced by the ramified covering of the complex upper half-plane. We get new results for non-split curves of prime level p>12: the curve Xns+(p) has no non-trivial automorphisms, whereas the curve Xns(p) has exactly one non-trivial automorphism. Moreover, as an immediate consequence of our results we compute the automorphism group of X0*(n):=X0(n)/W, where W is the group generated by the Atkin-Lehner involutions of X0(n) and n is a large enough square.
Gruppo di ricerca: Continuous Optimization
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