On Non-commutative Iwasawa Theory

Main Conjectures in non-commutative Iwasawa theory have been formulated over the last two decades by a number of authors, including Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. A proper understanding of these conjectures, and of their precise relationships with other conjectures in the literature, requires a suitable theory of leading terms of p-adic L-functions, and of their descent properties.

Such a theory has been developed by Burns and Venjakob, under certain hypotheses. The proposed research question asks whether the theory of Burns and Venjakob may be extended to new cases of interest.