Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

Mod $p$ Galois representations of solvable image
HTML articles powered by AMS MathViewer

by Hyunsuk Moon and Yuichiro Taguchi PDF
Proc. Amer. Math. Soc. 129 (2001), 2529-2534 Request permission

Abstract:

It is proved that, for a number field $K$ and a prime number $p$, there exist only finitely many isomorphism classes of continuous semisimple Galois representations of $K$ into $\operatorname {GL}_{d}(\overline {\mathbb {F}}_{p})$ of fixed dimension $d$ and bounded Artin conductor outside $p$ which have solvable images. Some auxiliary results are also proved.
References
  • Greg Anderson, Don Blasius, Robert Coleman, and George Zettler, On representations of the Weil group with bounded conductor, Forum Math. 6 (1994), no. 5, 537–545. MR 1295150, DOI 10.1515/form.1994.6.537
  • A. Ash and W. Sinnott, An analogue of Serre’s conjecture for Galois representations and Hecke eigenclasses in the mod-$p$ cohomology of $\mathrm {GL} (n, \mathbb {Z} )$, to appear in Duke Math. J.
  • Roger W. Carter, Simple groups of Lie type, Pure and Applied Mathematics, Vol. 28, John Wiley & Sons, London-New York-Sydney, 1972. MR 0407163
  • Roger W. Carter, Finite groups of Lie type, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1985. Conjugacy classes and complex characters; A Wiley-Interscience Publication. MR 794307
  • Jean-Marc Fontaine, Il n’y a pas de variété abélienne sur $\textbf {Z}$, Invent. Math. 81 (1985), no. 3, 515–538 (French). MR 807070, DOI 10.1007/BF01388584
  • G. Frey, E. Kani and H. Völklein, Curves with infinite $K$-rational geometric fundamental group, Aspects of Galois Theory, H. Völklein, P. Müller, D. Habater and J.G. Thompson (eds.), London Math. Soc. Lect. Note Ser., vol. 256, pp. 85–118.
  • David Goss, Basic structures of function field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 35, Springer-Verlag, Berlin, 1996. MR 1423131, DOI 10.1007/978-3-642-61480-4
  • M.J. Larsen and R. Pink, Finite subgroups of algebraic groups, preprint (1998).
  • H. Moon, Finiteness results on certain mod $p$ Galois representations, J. Number Theory 84 (2000), 156–165.
  • Jean-Pierre Serre, Groupes algébriques et corps de classes, Publications de l’Institut de Mathématique de l’Université de Nancago, VII, Hermann, Paris, 1959 (French). MR 0103191
  • J.-P. Serre, Corps Locaux, $3^{\text {e}}$ éd., Hermann, Paris, 1980.
  • Jean-Pierre Serre, Sur les représentations modulaires de degré $2$ de $\textrm {Gal}(\overline \textbf {Q}/\textbf {Q})$, Duke Math. J. 54 (1987), no. 1, 179–230 (French). MR 885783, DOI 10.1215/S0012-7094-87-05413-5
  • D. A. Suprunenko, Matrix groups, Translations of Mathematical Monographs, Vol. 45, American Mathematical Society, Providence, R.I., 1976. Translated from the Russian; Translation edited by K. A. Hirsch. MR 0390025, DOI 10.1090/mmono/045
  • Y. Taguchi, On Artin conductors of mod $\ell$ Galois representations, in preparation.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11R29, 11R32
  • Retrieve articles in all journals with MSC (2000): 11R29, 11R32
Additional Information
  • Hyunsuk Moon
  • Affiliation: Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan
  • Address at time of publication: Department of Mathematics, College of Natural Sciences, Seoul National University, Seoul, 151-742, Korea
  • Email: moon@math.sci.hokudai.ac.jp, hmoon@math2.snu.ac.kr
  • Yuichiro Taguchi
  • Affiliation: Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan
  • Email: taguchi@math.sci.hokudai.ac.jp
  • Received by editor(s): January 12, 2000
  • Published electronically: January 23, 2001
  • Communicated by: David E. Rohrlich
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 2529-2534
  • MSC (2000): Primary 11R29, 11R32
  • DOI: https://doi.org/10.1090/S0002-9939-01-05894-4
  • MathSciNet review: 1838373