Unconditional motivic Galois groups and Voevodsky's nilpotence conjecture in the noncommutative world, by Matilde Marcolli and Goncalo Tabuada

In this article we further the study of noncommutative pure motives. We construct unconditional noncommutative motivic Galois groups and relate them to the unconditional motivic Galois groups developed originally by Andre-Kahn. Then, we introduce the correct noncommutative analogue of Voevodsky's nilpotence conjecture and explore its interaction with the finite dimensionality of noncommutative Chow motives as well as with Voevodsky's original conjecture.

Matilde Marcolli <matilde@caltech.edu>
Goncalo Tabuada <tabuada@math.mit.edu>