Analytic Iwasawa invariants of higher weight modular forms

One can attach analytic and algebraic Iwasawa invariants μ and λ to a p-ordinary modular form of arbitrary weight. The analytic invariants neatly encode the p-adic valuations of special values of complex L-series; the algebraic invariants encode the size of various Selmer groups.

However, in the case of p-supersingular modular forms, such a theory of Iwasawa invariants does not yet exist. In the special case of weight 2, one can attach analytic and algebraic Iwasawa invariants μ⁺, μ^-, λ⁺ and λ^- which have properties similar to their ordinary analogues.

In this talk, we will study p-supersingular modular forms of weight p+1 and will give a definition of analytic Iwasawa invariants in this case. Moreover, we will propose a (highly) conjectural picture which should explain what is occurring on the algebraic side.

This project is joint with Tom Weston.