COURBES ELLIPTIQUES SEMI-STABLES SUR LES CORPS DE NOMBRES
2007 ◽
Vol 03
(04)
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pp. 611-633
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Let K be a number field. In this paper, we are interested in the following problem: does there exist a constant cK, which depends only on K, such that for any semi-stable elliptic curve defined over K, the Galois representation in its p-torsion points is irreducible whenever p is a prime number greater than cK? In case the answer is positive, how can we get such a constant? We prove that if a certain condition is satisfied by K, the answer is positive and we obtain cK explicitly. Furthermore, we prove that this condition is realized in many situations.
1984 ◽
Vol 96
◽
pp. 139-165
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2019 ◽
Vol 26
(1/2)
◽
pp. 227-231
2011 ◽
Vol 07
(04)
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pp. 1001-1032
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2015 ◽
Vol 11
(06)
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pp. 1725-1734
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2013 ◽
Vol 09
(07)
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pp. 1743-1752
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1988 ◽
Vol 109
◽
pp. 125-149
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2019 ◽
Vol 101
(2)
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pp. 238-246
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