A note on critical $p$-adic $L$-functions

Abstract

We study the adjunction property of the Jacquet-Emerton functor in certain neighborhoods of critical points in the eigencurve. As an application, we construct two-variable $p$-adic $L$-functions around critical points via Emerton's representation theoretic approach.

19 pages, to appear in Acta Mathematica Sinica, English Serie (Special Issue on Arithmetic Geometry)