DOCUMENTA MATHEMATICA, Vol. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 165-209

David Burns and Otmar Venjakob

On the Leading Terms of Zeta Isomorphisms and p-Adic L-functions in Non-Commutative Iwasawa Theory

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.

2000 Mathematics Subject Classification: Primary 11G40; Secondary 11R65 19A31 19B28

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