124 citations · 402 across the 57 of their papers we have counts for
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Noncommutative motives and their applications
Matilde Marcolli, Goncalo Tabuada
This survey is based on lectures given by the authors during the program "Noncommutative algebraic geometry and representation theory" at the MSRI, Berkeley, in the spring of 2013.…
Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives
Goncalo Tabuada
I. Panin proved in the nineties that the algebraic K-theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras. Later, Merkurjev and P…
Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives
Marcello Bernardara, Goncalo Tabuada
The Beilinson-Bloch type conjectures predict that the low degree rational Chow groups of intersections of quadrics are one dimensional. This conjecture was proved by Otwinowska. Ma…
Noncommutative motives of Azumaya algebras
Goncalo Tabuada, Michel Van den Bergh
Let k be a base commutative ring, R a commutative ring of coefficients, X a quasi-compact quasi-separated k-scheme, A a sheaf of Azumaya algebras over X of rank r, and Hmo(R) the c…
Weil transfer of noncommutative motives
Goncalo Tabuada
The Weil restriction functor, introduced in the late fifties, was recently extended by Karpenko to the category of Chow motives with integral coefficients. In this article we intro…
From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives
Marcello Bernardara, Goncalo Tabuada
Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the associated bounded derived categories of coherent sheaves. Assume the existence of a triangulated cate…