Mod 2 and mod 5 icosahedral representations
نویسندگان
چکیده
منابع مشابه
Mod 2 and Mod 5 Icosahedral Representations
We shall call a simple abelian variety A/Q modular if it is isogenous (over Q) to a factor of the Jacobian of a modular curve. In this paper we shall call a representation ρ̄ : GQ→GL2(F̄l) modular if there is a modular abelian variety A/Q, a number field F/Q of degree equal to dimA, an embedding OF ↪→ End(A/Q) and a homomorphism θ : OF→F̄l such that ρ̄ is equivalent to the action of GQ on the ker θ...
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We give eight new examples of icosahedral Galois representations that satisfy Artin’s conjecture on holomorphicity of their L-function. We give in detail one example of an icosahedral representation of conductor 1376 = 2 · 43 that satisfies Artin’s conjecture. We briefly explain the computations behind seven additional examples of conductors 2416 = 2 · 151, 3184 = 2 · 199, 3556 = 2 · 7 · 127, 3...
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In [Shepherd-Barron and Taylor 97] it is shown that for = 3 and 5 every odd, irreducible, two-dimensional Galois representation of Gal(Q̄/Q) with values in F and determinant the cyclotomic character is “elliptic,” i.e., it agrees with the representation given by the action of Gal(Q̄/Q) on the -torsion points of an elliptic curve defined over Q. In this note we will show that this is false for eve...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1997
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-97-00226-9