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$F$-split Galois representations are potentially abelian

Author(s): Chandrashekhar Khare
Journal: Proc. Amer. Math. Soc. 131 (2003), 3021-3023.
MSC (2000): Primary 11R32
Posted: February 20, 2003
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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:

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Henniart, G., Représentations $\ell$-adiques abéliennes, in Séminaire de Théorie des Nombres, Progress in Math. 22 (1982), 107-126, Birkhauser. MR 85d:11070

[KhRa]
Khare, C., Rajan, C. S., The density of ramified primes in semisimple $p$-adic Galois representations, International Mathematics Research Notices no. 12 (2001), 601-607. MR 2002e:11066

[LP]
Larsen, M., Pink, R., On $\ell$-independence of algebraic monodromy groups in compatible systems of representations, Invent. Math. 107 (1992), 603-636. MR 93h:22031

[Se]
Serre, J-P., Abelian $\ell$-adic representations and elliptic curves, Addison-Wesley, 1989. MR 91b:11071

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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: 10.1090/S0002-9939-03-06954-5
PII: S 0002-9939(03)06954-5
Received by editor(s): May 13, 2002
Posted: February 20, 2003
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2003, American Mathematical Society

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