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Iwasawa theory for modular forms at supersingular primes

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Let f = \sum a_n q^n be a normalised new form. If p is a supersingular prime for f, the classical p-adic L-functions have unbounded coefficients. In the case of a_p = 0, Pollack has defined plus and minus p-adic L-functions for f which have bounded coefficients. Generalising Kobayahsi’s work on elliptic curves, we will define Selmer subgroups which are cotorsion over the cyclotomic extension of Q and relate them to Pollack’s p-adic L-functions via the construction of Coleman maps. This enables us to state a version of the Iwasawa main conjecture.

This talk is part of the Number Theory Seminar series.

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