Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-02-06T12:41:55.095Z Has data issue: false hasContentIssue false
  • English
  • Français

REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR

Published online by Cambridge University Press:  24 January 2003

Richard Taylor
Richard Taylor
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
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.

We show that a continuous, odd, regular (non-exceptional), ordinary, irreducible, two-dimensional, $l$-adic representation of the absolute Galois group of the rational numbers is modular over some totally real field. We deduce that it occurs in the $l$-adic cohomology of some variety over the rationals and that its $L$-function has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.

AMS 2000 Mathematics subject classification: Primary 11F80. Secondary 11G40

Keywords

Galois representationmodularityFontaine–Mazur
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 1 , January 2002 , pp. 125 - 143
Copyright
2002 Cambridge University Press