124 citations · 402 across the 57 of their papers we have counts for
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HPD-invariance of the Tate, Beilinson and Parshin conjectures
Goncalo Tabuada
We prove that the Tate, Beilinson and Parshin conjectures are invariant under Homological Projective Duality (=HPD). As an application, we obtain a proof of these celebrated conjec…
On Grothendieck's standard conjectures of type C and D in positive characteristic
Goncalo Tabuada
Making use of topological periodic cyclic homology, we extend Grothendieck's standard conjectures of type C and D (with respect to crystalline cohomology theory) from smooth projec…
Schur-finiteness (and Bass-finiteness) conjecture for quadric fibrations and for families of sextic du Val del Pezzo surfaces
Goncalo Tabuada
Let Q -> B be a quadric fibration and T -> B a family of sextic du Val del Pezzo surfaces. Making use of the recent theory of noncommutative mixed motives, we establish a precise r…
HPD-invariance of the Tate conjecture
Goncalo Tabuada
We prove that the Tate conjecture is invariant under Homological Projective Duality (=HPD). As an application, we prove the Tate conjecture in the new cases of linear sections of d…
Noncommutative motives in positive characteristic and their applications
Goncalo Tabuada
Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology, we start by proving that the category of noncommutative numerical motives over…
Feynman quadrics-motive of the massive sunset graph
Matilde Marcolli, Goncalo Tabuada
We prove that the Feynman quadrics-motive of the massive sunset graph is "generically" not mixed-Tate. Moreover, we explicitly describe its "extra" complexity in terms of a Prym va…