Unit L-Functions for étale sheaves of modules over noncommutative rings

Abstract

Let s : X → Spec F be a separated scheme of finite type over a finite field F of characteristic p, let Λ be a not necessarily commutative Zpalgebra with finitely many elements, and let F • be a perfect complex of Λsheaves on the étale site of X. We show that the ratioWe use this to prove a version of the noncommmutative Iwasawa main conjecture for p-adic Lie coverings of X.

Iwasawa Theory 2012

“…By replacing F with its algebraic closure in the function field of X and using Lemma 6, we may assume that X is geometrically connected. In Witte (2013) we generalise this result to noncommutative Z p -algebras . The formula in Theorem 2 is also valid if is a finite field of characteristic p, see Deligne (1977, Fonction L mod`n, Theorem 2.2.(b)).…”

K1 of a p-adic group ring II. The determinantal kernel SK1

“…In Section 6.3, we also show that Corollary 1.9 implies: These and other similar results play an important role in the proof of the adelic Riemann-Roch theorem of [4] and in recent work of M. Witte [29].…”