Summary: In this paper, we consider the $\Lambda$-adic deformations of Galois representations associated to elliptic curves. We prove that the Pontryagin dual of the Selmer group of a $\Lambda$-adic deformation over certain $p$-adic Lie extensions of a number field, that are not necessarily commutative, has no non-zero pseudo-null submodule. We also study the structure of various arithmetic Iwasawa modules associated to such deformations.

14H52, 11F80, 11R34

elliptic curve, Galois representation, deformations, Galois cohomology, $p$-adic Lie extensions, Selmer groups