DOCUMENTA MATHEMATICA, Vol. 17 (2012), 573-606

Sudhanshu Shekhar and R. Sujatha

On the Structure of Selmer Groups of Lambda-Adic Deformations over p-Adic Lie Extensions

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.

2010 Mathematics Subject Classification: 14H52, 11F80, 11R34

Keywords and Phrases: Elliptic curve, Galois representation, deformations, Galois cohomology, $p$-adic Lie extensions, Selmer Groups.

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