On uniform lower bound of the Galois images associated to elliptic curves

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Let p be a prime and K be a number field. Let rho_{E,p}:G_K \longrightarrow Aut(T_p E)\cong GL_2(Z_p) be the Galois representation given by the Galois action on the p-adic Tate module of an elliptic curve E over K. Serre showed that the image of rho_{E,p} is open if E has no complex multiplication. For an elliptic curve E over K whose j-invariant does not appear in an exceptional finite set, we give an explicit uniform lower bound of the size of the image of rho_{E,p}.
41 pages

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Number Theory, 11G05

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http://salesiana.dossiersoluciones.com/handle/123456789/126241

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0703686
 http://arxiv.org/abs/math/0703686

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arXiv