Fundamental isomorphism conjecture via non‐commutative motives

Abstract

AbstractGiven a group, we construct a “fundamental localizing invariant” on its orbit category. We prove that any isomorphism conjecture valid for this fundamental invariant implies the same isomorphism conjecture for all localizing invariants, like non‐connective K‐theory, Hochschild homology, cyclic homology, and so on. Then, we discuss how to reduce such a fundamental isomorphism conjecture to essentially K‐theoretic ones. Finally, we develop the analogue additive results.