On a Conjecture of Watkins
نویسندگان
چکیده
Watkins has conjectured that if R is the rank of the group of rational points of an elliptic curve E over the rationals, then 2 divides the modular parametrisation degree. We show, for a certain class of E, chosen to make things as easy as possible, that this divisibility would follow from the statement that a certain 2adic deformation ring is isomorphic to a certain Hecke ring, and is a complete intersection. However, we show also that the method developed by Taylor, Wiles and others, to prove such statements, is necessarily inapplicable to our situation. It seems then that some new method is required if this approach to Watkins’ conjecture is to work.
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