Let f be a germ of plane curve, we define the ∂-degree of sufficiency of f to be the smallest integer τ such that for any germ g such that j(τ) f = j(τ)g then there is a set of disjoint annuii in S³ ...
We show that if E is an elliptic curve over Q with a Q-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to E is as large as allowed by the isogeny, except for ...
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