Galois descent of additive invariants

TL;DR

This paper proves that all additive invariants in noncommutative geometry satisfy Galois descent, unifying various homological and K-theoretic invariants under this property.

Contribution

It establishes Galois descent for a broad class of additive invariants using noncommutative motives, extending previous results to new invariants.

Findings

Additive invariants satisfy Galois descent.

Includes examples like Hochschild and cyclic homology.

Covers algebraic and topological K-theories.

Abstract

Making use of the recent theory of noncommutative motives, we prove that every additive invariant satisfies Galois descent. Examples include mixed complexes, Hochschild homology, cyclic homology, periodic cyclic homology, negative cyclic homology, connective algebraic K-theory, mod-l algebraic K-theory, nonconnective algebraic K-theory, homotopy K-theory, topological Hochschild homology, and topological cyclic homology.