A non-abelian Kummer congruence for L-functions of CM elliptic curves

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• Dohyeong Kim
• Tuesday 04 March 2014, 16:15-17:15
• MR13.

If you have a question about this talk, please contact James Newton.

In 2005, non-commutative Iwasawa theory was formulated by Coates, Kato, Fukaya, Kato, and Venjakob. It predicts that a p-adic L-function lies in the first algebraic K-group of certain localized Iwasawa algebra. As a consequence of it, one can predict various congruences between special values of twists of an L-function by various Artin representations, which we consider as non-abelian generalizations of the classical Kummer congruence. I will describe a concrete example of such arising from CM elliptic curves over false Tate curve extensions, and give a sketch of a proof using Hilbert modular forms.

This talk is part of the Number Theory Seminar series.

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