L-invariants and Darmon cycles attached to higher weight modular forms
Let f be a modular eigenform of even weight k=2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module DFMf and an L-invariant LFMf. The first goal of this paper is building a suitable p-...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/341108 |
| Acceso en línea: | https://hdl.handle.net/2117/341108 https://dx.doi.org/10.4171/JEMS/352 |
| Access Level: | acceso abierto |
| Palabra clave: | Arithmetical algebraic geometry Diophantine geometry Darmon point L-invariant Shimura curves quaternion algebra p-adic integration Geometria algèbrica--Aritmètica Anàlisi diofàntica Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Sumario: | Let f be a modular eigenform of even weight k=2 and new at a prime p dividing exactly the level with respect to an indefinite quaternion algebra. The theory of Fontaine-Mazur allows to attach to f a monodromy module DFMf and an L-invariant LFMf. The first goal of this paper is building a suitable p-adic integration theory that allows us to construct a new monodromy module Df and L-invariant Lf, in the spirit of Darmon. The two monodromy modules are isomorphic, and in particular the two L-invariants are equal. Let K be a real quadratic field and assume the sign of the functional equation of the L-series of f over K is -1. The Bloch-Beilinson conjectures suggest that there should be a supply of elements in the Selmer group of the motive attached to f over the tower of narrow ring class fields of K. Generalizing work of Darmon for k=2, we give a construction of local cohomology classes which we expect to arise from global classes and satisfy an explicit reciprocity law, accounting for the above prediction. |
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