Kontsevich's noncommutative numerical motives

TL;DR

This paper proves that Kontsevich's category of noncommutative numerical motives is equivalent to a previously constructed category, confirming its abelian semi-simple structure as conjectured.

Contribution

It establishes the equivalence of two constructions of noncommutative numerical motives and confirms their semi-simplicity.

Findings

NCnum is equivalent to the authors' constructed category.

NCnum is abelian semi-simple.

Confirms Kontsevich's conjecture on the structure of NCnum.

Abstract

In this note we prove that Kontsevich's category NCnum of noncommutative numerical motives is equivalent to the one constructed by the authors. As a consequence, we conclude that NCnum is abelian semi-simple as conjectured by Kontsevich.