We will construct a $p$-adic family of Saito-Kurokawa lifts for a Coleman family and extend the result of Agarwal and Brown on the Bloch-Kato conjecture for elliptic modular forms of low weights to higher weights. More precisely, we will prove that the $p$-valuation of the order of the Selmer group of a Coleman deformation is bounded below by the $p$-valuation of the algebraic part of the critical $L$-value attached to the initial Hecke eigenform of a Coleman family satisfying some reasonable assumptions given by Agarwal and Brown.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/7600