Iwasawa invariants of galois deformations

of the absolute Galois group of a number field F . Assume that ρ̄ is ordinary in the sense that the image of any decomposition group at a place v dividing p lies in some Borel subgroup Bv of G. Assume also that ρ̄ satisfies the conditions of [11, Section 7] which guarantee that it has a reasonable deformation theory; see Section 3.1 for details. In this paper we show that the Iwasawa invariants of the Selmer group of a nearly ordinary deformation of ρ̄ depends only on ρ̄ and the tame ramification of the deformation. For a precise statement, let H denote the set of nearly ordinary (with respect to the Bv) deformations of ρ̄ to continuous finitely ramified representations ρ : GF → G(O ) over the ring of integers O of the maximal totally ramified extension of K. Fix an algebraic representation r : G → GLn such that [F : Q] divides ∑