Mahesh Kakde (Princeton)

Congruences in non-commutative Iwasawa theory

In this talk I will discuss the results on computation of K₁ groups of certain Iwasawa algebras. I will sketch a strategy for deducing the non-commutative main conjecture of Iwasawa theory from results obtained from these computation and certain number theoretic input i.e. abelian main conjectures and certain congruences between abelian p-adic L-functions. I will discuss a case in which these congruences can be proven (for example Katz's p-adic L-function under certain assumptions).