On p-adic analogues of the Birch and Swinnerton-Dyer conjecture for Garrett L-functions

This article formulates a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for a p-adic L-function associated to a triple of Hida families of modular forms. This involves the construction of a p-adic regulator, obtained by building on Nekovář theory of Selmer complexes. Moreover, it is proved that our conjectures imply the “Elliptic Stark Conjectures” of Darmon, Lauder and Rotger.