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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPARENT, Pierre
dc.date.accessioned2024-04-04T03:11:18Z
dc.date.available2024-04-04T03:11:18Z
dc.date.created2016-07-01
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193764
dc.description.abstractEnWe develop a strategy for bounding from above the height of rational points of modular curves with values in number fields, by functions which are polynomial in the level. Our main technical tools come from effective arakelovian descriptions of modular curves and jacobians. We then fulfill this program in the following particular case: If~$p$ is a not-too-small prime number, let~$X_0 (p )$ be the classical modular curve of level $p$ over $\Q$. Assume Brumer's conjecture on the dimension of winding quotients of $J_0 (p)$. We prove that there is a function $b(p)=O(p^{13} )$ (depending only on $p$) such that, for any quadratic number field $K$, the $j$-height of points in $X_0 (p ) (K)$ which are not lift of elements of $X_0 (p)/w_p (\Q )$, is less or equal to~$b(p)$.
dc.language.isoen
dc.subject.enModular curves
dc.subject.enmodular jacobians
dc.subject.enArakelov theory
dc.subject.enarithmetic Bézout theorems
dc.title.enHeights on square of modular curves
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1606.09553v1
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01448316
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01448316v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=PARENT,%20Pierre&rft.genre=preprint


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