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Selmer groups of elliptic curves and Iwasawa algebras

Speaker: Jishnu Ray, Postdoctoral Researcher at CRM, Université de Montréal

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Abstract: The Selmer group of an elliptic curve over a number field encodes several arithmetic data of the curve providing a p-adic approach to the Birch and Swinnerton Dyer, connecting it with the p-adic L-function via the Iwasawa main conjecture. Under suitable extensions of the number field, the dual Selmer group becomes a module over the Iwasawa algebra of a certain compact p-adic Lie group over Z_p (the ring of p-adic integers), which is a completed group algebra.

In this talk, we give an explicit ring-theoretic presentation, by generators and relations, of Iwasawa algebras and explore the structure of Selmer groups over non-commutative Lie extensions.

 

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