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We study the variation of the dimension of the Bloch-Kato Selmer group of ap-adic Galois representation of a number field that varies in a refined family.We show that, if one restricts ourselves to representations that are, at everyplace dividing $p$, crystalline, non-critically refined, and with a fixednumber of non-negative Hodge-Tate weights, then the dimension of the Selmergroup varies essentially lower-semi-continuously. This allows to prove lowerbounds for Selmer groups "by continuity", in particular to prove somepredictions of the conjecture of Bloch-Kato for modular forms.

Ranks of Selmer groups in an analytic family