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Presented By: Department of Mathematics

Group, Lie and Number Theory Seminar

Bi-ordinary modular forms

It is known that p-ordinary cuspidal Hecke eigenforms give rise to 2-dimensional global Galois representations which become reducible after restriction to a decomposition group at p. For which such forms is this restriction not only reducible but also splittable? Complex multiplication (CM) forms satisfy this p-local property, but such a restrictive global property as CM necessary? In classical weights at least 2, it is expected that this is the case. We present a construction of "bi-ordinary" p-adic modular forms, which can measure exceptions to this expectation. We also give evidence that there are non-CM but p-locally splittable forms in p-adic weights. This is joint work with Francesc Castella. Speaker(s): Carl Wang-Erickson (University of Pittsburgh)

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