Completed cohomology of Shimura curves and a p-adic Jacquet–Langlands correspondence
J Newton - Mathematische Annalen, 2013 - Springer
We study indefinite quaternion algebras over totally real fields F, and give an example of a
cohomological construction of p-adic Jacquet–Langlands functoriality using completed …
cohomological construction of p-adic Jacquet–Langlands functoriality using completed …
Quantitative level lowering for weight two Hilbert modular forms
M Moakher - arXiv preprint arXiv:2408.15410, 2024 - arxiv.org
We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by
Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the …
Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the …
Local to global compatibility on the eigencurve
AGM Paulin - Proceedings of the London Mathematical Society, 2011 - Wiley Online Library
We generalize Coleman's construction of Hecke operators in families to define an action of
GL 2 (A fp) on the space of overconvergent p‐adic modular forms, extending the classical …
GL 2 (A fp) on the space of overconvergent p‐adic modular forms, extending the classical …
Geometric level raising and lowering on the eigencurve
AGM Paulin - manuscripta mathematica, 2012 - Springer
If π f is a cuspidal automorphic representation of GL_ 2/Q associated to a modular form f, the
local and global Langlands correspondences are compatible at all finite places of Q. On the …
local and global Langlands correspondences are compatible at all finite places of Q. On the …
Level raising and completed cohomology
J Newton - International Mathematics Research Notices, 2011 - ieeexplore.ieee.org
We describe an application of Poincaré duality for completed homology spaces (as defined
by Emerton) to level raising for p-adic modular forms. This allows us to give a new …
by Emerton) to level raising for p-adic modular forms. This allows us to give a new …
Failure of the local to global principle in the eigencurve
AGM Paulin - arXiv preprint arXiv:1001.2051, 2010 - arxiv.org
For a cuspidal automorphic representation of GL2/Q associated to a modular form, the local
and global Langlands correspondences are compatible at all finite places of Q. On the p …
and global Langlands correspondences are compatible at all finite places of Q. On the p …
Level raising for -adic Hilbert modular forms
J Newton - Journal de théorie des nombres de Bordeaux, 2016 - jtnb.centre-mersenne.org
This paper generalises previous work of the author to the setting of overconvergent p-adic
automorphic forms for a definite quaternion algebra over a totally real field. We prove results …
automorphic forms for a definite quaternion algebra over a totally real field. We prove results …