Noncommutative Quillen-Lichtenbaum Conjecture

TL;DR

This paper extends the classical Quillen-Lichtenbaum conjecture to separated complex schemes and introduces a noncommutative geometric perspective, establishing isomorphism ranges for algebraic and topological K-groups.

Contribution

It generalizes the conjecture via noncommutative geometry and refines the isomorphism ranges for algebraic and topological K-groups in complex schemes.

Findings

Established isomorphism ranges for algebraic and topological K-groups.

Extended the classical conjecture to separated complex schemes of finite type.

Generalized the conjecture through noncommutative geometric methods.

Abstract

We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we generalizes the conjecture through the lens of noncommutative geometry.