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Number Theory Seminar

Thursday, March 12, 2020
4:00pm to 5:00pm
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Linde Hall 387
Bi-ordinary modular forms
Carl Wang-Erickson, Department of Mathematics, University of Pittsburgh,

It is well-understood that p-ordinary Hecke eigenforms give rise to global 2-dimensional Galois representations which become reducible with an unramified quotient after restriction to a decomposition group at p. Coleman and Greenberg independently asked for a characterization of those p-ordinary forms whose associated Galois representation is also semi-simple after restriction to this decomposition group. It has been suspected that all such p-ordinary forms have complex multiplication, a restrictive global property. We will discuss joint work with Francesc Castella, in which we give a criterion for this suspicion to be true, and give a construction of "bi-ordinary" modular forms as a tool to explore the case that the criterion fails.

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