124 citations · 402 across the 57 of their papers we have counts for
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Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras
Goncalo Tabuada
We start by developing a theory of noncommutative (=NC) mixed motives with coefficients in any commutative ring. In particular, we construct a symmetric monoidal triangulated categ…
Noncommutative motives of separable algebras
Goncalo Tabuada, Michel Van den Bergh
In this article we study in detail the category of noncommutative motives of separable algebras Sep(k) over a base field k. We start by constructing four different models of the fu…
Exponentiation of motivic measures
Niranjan Ramachandran, Goncalo Tabuada
In this short note we establish some properties of all those motivic measures which can be exponentiated. As a first application, we show that the rationality of Kapranov's zeta fu…
Some remarks concerning Voevodsky's nilpotence conjecture
Marcello Bernardara, Matilde Marcolli, Goncalo Tabuada
In this note we extend Voevodsky's nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories. Making use of this noncommutative gen…
A1-homotopy theory of noncommutative motives
Goncalo Tabuada
In this article we continue the development of a theory of noncommutative motives. We construct categories of A1-homotopy noncommutative motives, described their universal properti…
Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives
Goncalo Tabuada
Following an insight of Kontsevich, we prove that the quotient of Voevodsky's category of geometric mixed motives DM by the endofunctor -Q(1)[2] embeds fully-faithfully into Kontse…