Images of Galois representations in mod p Hecke algebras
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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21
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International Journal of Number Theory, Volume 17, issue 5, pp. 1265-1285
Abstract
Let (f, f) denote the mod p local Hecke algebra attached to a normalized Hecke eigenform f, which is a commutative algebra over some finite field q of characteristic p and with residue field q. By a result of Carayol we know that, if the residual Galois representation ρ¯f: G →GL2(q) is absolutely irreducible, then one can attach to this algebra a Galois representation ρf: G →GL2(f) that is a lift of ρ¯f. We will show how one can determine the image of ρf under the assumptions that (i) the image of the residual representation contains SL2(q), (ii) f2 = 0 and (iii) the coefficient ring is generated by the traces. As an application we will see that the methods that we use allow to deduce the existence of certain p-elementary abelian extensions of big non-solvable number fields.Description
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Amorós, L 2021, 'Images of Galois representations in mod p Hecke algebras', International Journal of Number Theory, vol. 17, no. 5, pp. 1265-1285. https://doi.org/10.1142/S1793042121500354