On the leading terms of zeta isomorphisms and $p$-adic $L$-functions in non-commutative Iwasawa theory

Abstract

We discuss the formalism of Iwasawa theory descent in the setting of the localized $K_1$-groups of Fukaya and Kato. We then prove interpolation formulas for the 'leading terms' of the global Zeta isomorphisms that are associated to certain Tate motives and of the $p$-adic $L$-functions that are associated to certain critical motives.