Abstract
We study the variation of the dimension of the Bloch-Kato Selmer group of a p-adic Galois representation of a number field that varies in a refined family. We show that, if we restrict ourselves to representations that are, at every place dividing p, crystalline, non-critically refined, and with a fixed number of non-negative Hodge-Tate weights, then the dimension of the Selmer group varies essentially lower-semi-continuously. This allows us to prove lower bounds for Selmer groups "by continuity", and in particular to deduce from a result of Bellaiche and Chenevier that the p-adic Selmer group of a modular eigenform of weight 2 of sign -1 has rank at least 1.