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Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ( k ) F of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ( k ) F is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...

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