Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


On modular forms and the inverse Galois problem
HTML articles powered by AMS MathViewer

by Luis Dieulefait and Gabor Wiese PDF
Trans. Amer. Math. Soc. 363 (2011), 4569-4584 Request permission


In this article new cases of the inverse Galois problem are established. The main result is that for a fixed integer $n$, there is a positive density set of primes $p$ such that $\mathrm {PSL}_2(\mathbb {F}_{p^n})$ occurs as the Galois group of some finite extension of the rational numbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their residual Galois representations are as large as a priori possible. Both results essentially use Khare’s and Wintenberger’s notion of good-dihedral primes. Particular care is taken in order to exclude nontrivial inner twists.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11F80, 12F12, 11F11
  • Retrieve articles in all journals with MSC (2010): 11F80, 12F12, 11F11
Additional Information
  • Luis Dieulefait
  • Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
  • MR Author ID: 671876
  • Email:
  • Gabor Wiese
  • Affiliation: Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Ellernstraße 29, 45326 Essen, Germany
  • Email:
  • Received by editor(s): May 26, 2009
  • Published electronically: April 11, 2011
  • Additional Notes: The first author was partially supported by the grant MTM2009-07024 from the Ministerio de Ciencia e Innovación (Spain).
    The second author acknowledges partial support by the Sonderforschungsbereich Transregio 45 of the Deutsche Forschungsgemeinschaft. Both authors were partially supported by the European Research Training Network Galois Theory and Explicit Methods MRTN-CT-2006-035495.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 4569-4584
  • MSC (2010): Primary 11F80; Secondary 12F12, 11F11
  • DOI:
  • MathSciNet review: 2806684