Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-28T06:07:57.013Z Has data issue: false hasContentIssue false

Nearly ordinary rank four Galois representations and $p$-adic Siegel modular forms

Published online by Cambridge University Press:  25 September 2006

J. Tilouine
Affiliation:
Département de Mathématiques, UMR 7539, Institut Galilée, Université de Paris 13, 93430 Villetaneuse, Francetilouine@math.univ-paris13.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is devoted to the proof of two results. The first was conjectured in 1994 by the author. It concerns the identity, under certain assumptions, of the universal deformation ring of $p$-nearly ordinary Galois representations and a local component of the universal nearly ordinary Hecke algebra in the sense of Hida. The other, which relies on the first, concerns the modularity of certain abelian surfaces. More precisely, one can associate to certain irreducible abelian surfaces defined over the rationals overconvergent $p$-adic cusp eigenforms. The question of whether these forms are classical is not studied in this paper.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2006

Footnotes

With an appendix by Don Blasius