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Abstract |
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Iwasawa theory provides a mysterious connection between the (p-adic) analytic world and the mathematically faraway algebraic world. In the 1970s, B. Mazur formulated a version of this theory for elliptic curves by giving a conjectural connection between an analytic object of the elliptic curve (a p-adic L-function) and an algebraic one (a Selmer group) when p has (good) ordinary reduction. For the supersingular case, no truly analogous formulation was known until earlier this decade, when the corresponding faraway objects were discovered by two faraway mathematicians - R. Pollack constructed a pair of p-adic L-functions, and S. Kobayashi introduced a corresponding pair of Selmer groups. Both worked under the hypothesis that the trace of Frobenius vanished (i.e. a_p=0). In this talk, we present a tandem method that leads to a generalization to the non-vanishing case. |