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$F$-split Galois representations are potentially abelian


Author: Chandrashekhar Khare
Journal: Proc. Amer. Math. Soc. 131 (2003), 3021-3023
MSC (2000): Primary 11R32
Published electronically: February 20, 2003
MathSciNet review: 1993208
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Abstract: In this note we relate the property of a semisimple $\ell$-adic Galois representation being ``$F$-split'' to its having abelian image.


References [Enhancements On Off] (What's this?)

  • [H] Guy Henniart, Représentations 𝑙-adiques abéliennes, Seminar on Number Theory, Paris 1980-81 (Paris, 1980/1981) Progr. Math., vol. 22, Birkhäuser Boston, Boston, MA, 1982, pp. 107–126 (French). MR 693314
  • [KhRa] Chandrashekhar Khare and C. S. Rajan, The density of ramified primes in semisimple 𝑝-adic Galois representations, Internat. Math. Res. Notices 12 (2001), 601–607. MR 1836789, 10.1155/S1073792801000319
  • [LP] M. Larsen and R. Pink, On 𝑙-independence of algebraic monodromy groups in compatible systems of representations, Invent. Math. 107 (1992), no. 3, 603–636. MR 1150604, 10.1007/BF01231904
  • [Se] Jean-Pierre Serre, Abelian 𝑙-adic representations and elliptic curves, 2nd ed., Advanced Book Classics, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. With the collaboration of Willem Kuyk and John Labute. MR 1043865

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Additional Information

Chandrashekhar Khare
Affiliation: Department of Mathematics, University of Utah, 155 S 1400 E, Salt lake City, Utah 84112
Address at time of publication: School of Mathematics, TIFR, Homi Bhabha Road, Mumbai 400 005, India
Email: shekhar@math.utah.edu, shekhar@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06954-5
Received by editor(s): May 13, 2002
Published electronically: February 20, 2003
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2003 American Mathematical Society