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Number Theory Seminar

Thursday, March 5, 2020
4:00pm to 5:00pm
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Linde Hall 387
Tame derivatives and the Eisenstein ideal
Preston Wake, Department of Mathematics, Michigan State University,

As was made famous by Mazur, the mod-5 Galois representation associated to the elliptic curve X_0(11) is reducible. Less famously, but also noted by Mazur, the mod-25 Galois representation is reducible. We'll talk about this kind of extra reducibility phenomenon more generally, for cuspforms of even weight k and prime level. We'll observe that the characters appearing in the reducible representation are related, on one hand, to an algebraic invariant (the ‘tame deriviative' of an L-function), and, on the other hand, to an algebraic invariant (the 'tame L-invariant'). This type of 'algebraic=analytic' relation is predicted by a version of the Bloch-Kato conjecture for families of motives formulated by Kato .

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].