Multiplicative isogeny estimates
1998 ◽
Vol 64
(2)
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pp. 178-194
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AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’. We find that in general the answer is no (Theorem 1), but that sometimes the answer is yes (Theorem 2). Further we apply the affirmative result to the study of exceptional primes ℒ in connexion with modular Galois representations coming from elliptic curves: we prove that the additive bounds for ℒ of Masser and Wüstholz (1993) can be improved to multiplicative bounds (Theorem 3).
2013 ◽
Vol 13
(3)
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pp. 517-559
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Keyword(s):
2015 ◽
Vol 151
(9)
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pp. 1626-1646
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Keyword(s):
1998 ◽
Vol 126
(10)
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pp. 2855-2856
2013 ◽
Vol 133
(10)
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pp. 3381-3393
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Keyword(s):
2016 ◽
Vol 102
(3)
◽
pp. 316-330
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2015 ◽
Vol 91
(10)
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pp. 141-146