On some l-adic representations of Gal(Qbar/Q) attached to noncongruence subgroups

Details On some l-adic representations of Gal(Qbar/Q) attached to noncongruence subgroups On some l-adic representations of Gal(Qbar/Q) attached to noncongruence subgroups

2004-02-07

arxiv.org/abs/math/0402111v2

Bulletin of the London Mathematical Society 2006 38(4):561-567

Mathematics

Number Theory

7 pages, now in LaTeX; some minor corrections

Scientific paper

10.1112/S002460930601856X

The l-adic parabolic cohomology groups attached to noncongruence subgroups of SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number field F. We exhibit examples (with F=Q) giving rise to Galois representations whose images are open subgroups of the full group of symplectic similitudes (of arbitrary dimension). The determination of the image of the Galois group relies on Katz's classification theorem for reductive subalgebras of gl(N) containing a principal nilpotent element; the paper also contains a short conceptual proof of this theorem, suggested by I. Gronowski.

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