p-adic and archimedean equidistribution of arithmetic cycles

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dc.catalogadorpau
dc.contributor.advisorMenares, Ricardo
dc.contributor.authorPérez Piña, Patricio
dc.contributor.otherPontificia Universidad Católica de Chile. Facultad de Matemáticas
dc.date.accessioned2025-06-03T15:36:35Z
dc.date.available2025-06-03T15:36:35Z
dc.date.issued2024
dc.date.updated2025-05-28T18:20:16Z
dc.descriptionTesis (Doctor en Matemáticas)--Pontificia Universidad Católica de Chile, 2024
dc.description.abstractThe purpose of this manuscript is to describe various equidistribution problems related to arithmetic cycles. Depending on the case, the context is p-adic, archimedean or S-arithmetic. The starting point for this research is Duke's equidistribution theorem. Our first result is a p-adic analogue for this theorem in the case of closed modular geodesics. The techniques employed for this are strong enough to obtain other equidistribution results such as: equidistribution of CM points on the p-adic points of a Shimura curve ramified at p; equidistribution of ATR cycles on Hilbert varieties; equidistribution of Stark-Heegner cycles in the mock Hilbert modular surface. The first chapter is an Introduction for our motivations and main results. The next two chapters are devoted to the proof our theorems. There is also an Appendix deepening in the notion of p-adic geodesics.
dc.description.funderANID
dc.description.funderBourse d’excellence de la Confederation suisse
dc.description.sponsorship21200911
dc.description.sponsorship2022.0414
dc.fechaingreso.objetodigital2025-06-02
dc.format.extent42 páginas
dc.fuente.origenAutoarchivo
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/104561
dc.information.autorucFacultad de Matemáticas; Menares, Ricardo; 0000-0001-5819-5347; 1008987
dc.information.autorucFacultad de Matemáticas; Pérez Piña, Patricio; S/I; 1139371
dc.language.isoen
dc.nota.accesocontenido completo
dc.rightsacceso abierto
dc.rights.licenseAtribución 4.0 Internacional (CC BY 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/deed.es
dc.subject.ddc510
dc.subject.deweyMatemática física y químicaes_ES
dc.titlep-adic and archimedean equidistribution of arithmetic cycles
dc.typetesis doctoral
sipa.codpersvinculados1008987
sipa.codpersvinculados1139371
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