Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-18T16:01:59.915Z 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
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)