Chennai Mathematical Institute


3.30 pm, Seminar Hall
Triangulation at the boundary of eigencurve

Aditya Karnataki
BICMR, Peking University, Beijing, China.


The classical eigencurve is a rigid analytic space parametrizing $p$-adic families of Hecke eigensystems associated to overconvergent modular forms of fixed tame level $N$ and a prime $p$. Recently, Andreatta, Iovita, and Pilloni constructed an integral model for the eigencurve. This allows access to the `points at boundary' of the eigencurve, which are associated to `$T$-adic modular forms'. These are mysterious objects whose properties deserve further study. We explain in this talk how to extend one such property, viz. triangulation, to the boundary points. This is joint work with Ruochuan Liu.