Gonçalo Nery Tabuada
Mathematics Institute Zeeman Building University of Warwick Coventry CV4 7AL United Kingdom
goncalo.tabuada@warwick.ac.uk
Office: C1.23 
[Preprints]
Grothendieck classes of quadric hypersurfaces and involution varieties [pdf] To appear in the volume in honor of Yuri I. Manin
Motivic AtiyahSegal completion theorem [pdf]
with Michel Van den Bergh Jacques Tits motivic measure [pdf] To appear in Mathematische Annalen Noncommutative Weil conjecture [pdf] To appear in Advances in Mathematics Noncommutative Riemann hypothesis [pdf] To appear in Proceedings of the American Mathematical Society HPDinvariance of the Tate conjecture(s) [pdf] To appear in Journal of Noncommutative Geometry 
[Publications]
Schurfiniteness (and Bassfiniteness) conjecture for quadric fibrations and for families of sextic du Val del Pezzo surfaces [link] Documenta Mathematica, 25 (2020), 23392354 Embedding of the derived Brauer group into the secondary Ktheory ring [link] Journal of Noncommutative Geometry, 14 (2020), 773788 Motivic
concentration theorem [link]
with Michel Van den Bergh Mathematical Research Letters, 27 (2020), no. 2, 565589 Noncommutative motives in positive
characteristic and their applications [link]
Advances in Mathematics, 349 (2019), 648681 Vanishing of the negative homotopy Ktheory of quotient singularities [link] Journal of the Institute of Mathematics of Jussieu, 18 (2019), no. 3, 619627 On Grothendieck's standard
conjectures of type C and D in positive characteristic
[link]
Proceedings of the American Mathematical Society 147 (2019), no. 12, 50395054 Feynman quadricsmotive of the massive sunset graph [link] with Matilde Marcolli Journal of Number Theory, 195 (2019), 159183 A note on the Schurfiniteness of linear sections [link] Mathematical Research Letters, 25 (2018), no. 1, 237253 Invariants of noncommutative projective schemes [link] Moscow Mathematical Journal, 18 (2018), no. 4, 787797 Noncommutative rigidity [link] Mathematische Zeitschrift, 289 (2018), no. 3, 12811298 A note on Grothendieck's standard conjectures of type C and D [link] Proceedings of the American Mathematical Society, 146 (2018), no. 4, 13891399 Equivariant noncommutative motives [link] Annals of Ktheory, 3 (2018), no. 1, 125156 Additive invariants of orbifolds [link] with Michel Van den Bergh Geometry and Topology, 22 (2018), 30033048 Some remarks concerning Voevodsky's nilpotence conjecture [link] with Marcello Bernardara and Matilde Marcolli Journal für die reine und angewandte Mathematik, 738 (2018), 299312 The Gysin triangle via localization and A^1homotopy invariance [link] with Michel Van den Bergh Transactions of the American Mathematical Society, 370 (2018), no. 1, 421446 Modified mixed realizations, new additive invariants, and periods of dg categories [link] International Mathematics Research Notices, 34 (2017), 76077638 A^1homotopy invariance of algebraic Ktheory with coefficients and du Val singularities [link] Annals of Ktheory, 2 (2017), no. 1, 125 Kimurafiniteness of quadric fibrations over smooth curves [link] C. R. Math. Acad. Sci. Paris, 355 (2017), 628632 (presented by Christophe Soulé) A^1homotopy invariants of corner skew Laurent polynomial algebras [link] Journal of Noncommutative Geometry 11 (2017), no. 4, 16271643 Picard groups, weight structures, and (noncommutative) mixed motives [link] with Mikhail Bondarko Documenta Mathematica 22 (2017), 4566 BostConnes systems, Categorification, Quantum statistical mechanics, and Weil numbers [link] with Matilde Marcolli Journal of Noncommutative Geometry 11 (2017), no. 1, 149 A note on secondary Ktheory [link] Algebra and Number Theory, 10 (2016), no. 4, 887906 Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras [link] Selecta Mathematica, 22 (2016), no. 2, 735764 Algebraic Ktheory with coefficients of cyclic quotient singularities [link] C. R. Math. Acad. Sci. Paris, 354 (2016), 449452 (presented by Michel Duflo) Noncommutative numerical motives, Tannakian structures, and motivic Galois groups [link] with Matilde Marcolli Journal of the European Mathematical Society 18 (2016), 623655 Noncommutative motives of separable algebras [link] with Michel Van den Bergh Advances in Mathematics, 303 (2016), 11221161 Ktheory of endomorphisms via noncommutative motives [link] with Andrew Blumberg and David Gepner Transactions of the American Mathematical Society 368 (2016), no. 2, 14351465 From semiorthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives [link] with Marcello Bernardara Moscow Mathematical Journal, 16 (2016), no. 2, 205235 Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives [link] with Marcello Bernardara Izv. Ross. Akad. Nauk. Ser. Mat. 80 (2016), no. 3, 322 A^1homotopy theory of noncommutative motives [link] Journal of Noncommutative Geometry 9 (2015), no. 3, 851875 Bivariant cyclic cohomology and Connes' bilinear pairings in noncommutative motives [link] Journal of Noncommutative Geometry 9 (2015), no. 2, 265285 Exponentiation of motivic measures [link] with Niranjan Ramachandran Journal of the Ramanujan Mathematical Society 30, (2015), no. 4, 349360 Weil restriction of noncommutative motives [link] Journal of Algebra, 430 (2015), 119152 A^1homotopy invariants of dg orbit categories [link] Journal of Algebra, 434 (2015), 169192 From exceptional collections to motivic decompositions via noncommutative motives [link] with Matilde Marcolli Journal für die reine und angewandte Mathematik 701 (2015), 153167 Unconditional noncommutative motivic Galois groups [link] with Matilde Marcolli Hodge theory and classical algebraic geometry. Contemporary Mathematics 647 (2015), 109115 Noncommutative motives of Azumaya algebras [link] with Michel Van den Bergh Journal of the Institute of Mathematics of Jussieu, 14 (2015), no. 2, 379403 Relations between the Chow motive and the noncommutative motive of a smooth projective variety [link] with Marcello Bernardara Journal of Pure and Applied Algebra, 219 (2015), no. 11, 50685077 Voevodsky's mixed motives
versus Kontsevich's noncommutative mixed motives [link]
Advances in Mathematics, 264 (2014), 506545 Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives [link] Journal of Algebra, 417 (2014), 1538 A Quillen model for classical Morita theory and a tensor categorification of the Brauer group [link] with Ivo Dell'Ambrogio Journal of Pure and Applied Algebra, 218 (2014), no. 12, 23372355 Uniqueness of the multiplicative cyclotomic trace [link] with Andrew Blumberg and David Gepner Advances in Mathematics, 260 (2014), 191232 Jacobians of noncommutative motives [link] with Matilde Marcolli Moscow Mathematical Journal, 14 (2014), no. 3, 577594 Galois descent of additive invariants [link] Bulletin of the London Mathematical Society, 46 (2014), no. 2, 385395 E_nregularity implies E_(n1)regularity [link] Documenta Mathematica, 19 (2014), 121139 Witt vectors and Ktheory of automorphisms via noncommutative motives [link] Manuscripta Mathematica, 143 (2014), no. 34, 473482 Noncommutative motives, numerical equivalence, and semisimplicity [link] with Matilde Marcolli American Journal of Mathematics, 136 (2014), no. 1, 5975 Noncommutative Artin motives [link] with Matilde Marcolli Selecta Mathematica, 20 (2014), 315358 Morita homotopy theory of C*categories [link] with Ivo Dell'Ambrogio Journal of Algebra, 398 (2014), 162199 Lefschetz and HirzebruchRiemannRoch formulas via noncommutative motives [link] with DenisCharles Cisinski Journal of Noncommutative Geometry 8 (2014), no. 4, 11711190 Chow motives versus noncommutative motives [link] Journal of Noncommutative Geometry 7 (2013), no. 3, 767786 Fundamental isomorphism conjecture via noncommutative motives [link] with Paul Balmer Mathematische Nachrichten, 286 (2013), no. 89, 791798 A universal characterization of higher algebraic Ktheory [link] with Andrew Blumberg and David Gepner Geometry and Topology, 17 (2013), 733838 Weil cohomologies and derived dg categories [link] Journal of Pure and Applied Algebra, 217 (2013), 12941302 Products, multiplicative Chern characters, and finite coefficients via noncommutative motives [link] Journal of Pure and Applied Algebra, 217 (2013), 12791293 Kontsevich's noncommutative numerical motives [link] with Matilde Marcolli Compositio Mathematica, 148 (2012), 18111820 Weight structure on Kontsevich's noncommutative mixed motives [link] Homology, Homotopy and Applications, 14(2) (2012), 129142 The fundamental theorem via derived Morita invariance, localization, and A^1homotopy invariance [link] Journal of KTheory, 9 (2012), no. 3, 407420 Transfer maps and projection formulas [link] Proceedings of the American Mathematical Society, 140 (2012), 25892597 Symmetric monoidal structure on noncommutative motives [link] with DenisCharles Cisinski Journal of KTheory, 9 (2012), no. 2, 201268 Tensor triangular geometry of noncommutative motives [link] with Ivo Dell'Ambrogio Advances in Mathematics, 229 (2012), no. 2, 13291357 Corepresentability of the Grothendieck group of endomorphisms functor in the category of noncommutative motives [link] Homology, Homotopy and Applications, 13(2) (2011), 315328 Universal suspension via noncommutative motives [link] Journal of Noncommutative Geometry 5 (2011), no. 4, 573589 A simple criterion for extending natural transformations to higher Ktheory [link] Documenta Mathematica 16 (2011), 657668 Nonconnective Ktheory via universal invariants [link] with DenisCharles Cisinski Compositio Mathematica 147 (2011), 12811320 A universal characterization of the Chern character maps [link] Proceedings of the American Mathematical Society 139 (2011), 12631271 On Drinfeld's DG quotient [link] Journal of Algebra, 323 (2010), 12261240 Homotopy theory of dg
categories via localizing pairs and Drinfeld's DG
quotient [link]
Homology, Homotopy and Applications, 12(1) (2010), 187219 Matrix invariants of spectral categories [link] International Mathematics Research Notices, 13 (2010), 24592511 Generalized spectral categories, topological Hochschild homology, and trace maps [link] Algebraic and Geometric Topology, 10 (2010), 137213 Differential graded versus simplicial categories [link] Topology and its Applications, 157 (2010), no. 3, 563593 Postnikov towers, kinvariants and obstruction theory for dg categories [link] Journal of Algebra, 321 (2009), no. 12, 38503877 Homotopy theory of spectral categories [link] Advances in Mathematics, 221 (2009), no. 4, 11221143 Noncommutative AndréQuillen cohomology for differential graded categories [link] Journal of Algebra, 321 (2009), no. 10, 29262942 Homotopy theory of wellgenerated algebraic triangulated categories [link] Journal of KTheory, 3 (2009), no. 1, 5375 Higher Ktheory via universal invariants [link] Duke Mathematical Journal, 145 (2008), no. 1, 121206 On the structure of CalabiYau categories with a cluster tilting subcategory [link] Documenta Mathematica, 12 (2007), 193213 Additive invariants of dg categories [link] International Mathematics Research Notices 53 (2005), 33093339 Addendum: International Mathematics Research Notices (2006), Art. ID 75853 Errata: International Mathematics Research Notices 24 (2007), Art. ID rnm149 (in french) A Quillen model structure on the category of dg categories [link] C. R. Math. Acad. Sci. Paris, 340 (2005), 1519 (presented by Christophe Soulé) (in french) 
[Surveys]
Noncommutative counterparts of celebrated conjectures [link] Ktheory in Algebra, Analysis and Topology (satellite event of the ICM 2018) Contemporary Mathematics 749 (2020), 353377 Recent developments on noncommutative motives [link] New Directions in Homotopy Theory, Contemporary Mathematics 707 (2018), 143173 Noncommutative motives and their
applications [link]
with Matilde Marcolli Commutative Algebra and Noncommutative Algebraic Geometry I, MSRI Publications 67 (2015), 191214 A guided tour through the garden of
noncommutative motives [link]
Clay Mathematics Proceedings, 16 (2012), 259276 
University Lecture Series 63,
American Mathematical Society, 2015

[Talks]
Conference Witt vectors in Algebra and Geometry, Moscow, Russia October 2022 Conference Noncommutative shapes (in honor of Michel Van den Bergh's 61th birthday), Antwerp, Belgium September 2022 Workshop Algebraic cycles, strings and amplitudes, Isaac Newton Institute, Cambridge, United Kingdom July 2022 W. Killing and K. Weierstrass Colloquium, Gdańsk, Poland July 2022 Online seminar Quadratic forms, linear algebraic groups and beyond July 2022 Algebra seminar, Institut de Mathématiques de Jussieu, Paris, France February 2022 Workshop Homotopical Algebra and Higher Structures, Oberwolfach, Germany September 2021 Portuguese Mathematical Society meeting (80th birthday celebration), Lisbon, Portugal July 2021 Noncommutative Geometry and Topology seminar, Czech Academy of Sciences, Prague, Czech Republic June 2021 New York City Noncommutative
Geometry
seminar,
New
York,
United
States
January 2021 Workshop Noncommutative motives and telescopetype problems, Hausdorff Research Institute for Mathematics, Bonn, Germany December 2020 Algebraic Topology seminar, University of Warwick, United Kingdom December 2020 Seminar on Algebra, Geometry and Physics, MaxPlanckInstitut für Mathematik, Germany August 2020 Summer school Motivic, equivariant, and noncommutative homotopy theory, IHÉS, France (Threelecture course) July 2020 JAMI Workshop RiemannRoch in characteristic one and related topics, Johns Hopkins University, United States October 2019 Conference The geometry of derived categories, Liverpool, United Kingdom September 2019 Workshop Algebraic Ktheory, Oberwolfach, Germany June 2019 Algebraic Geometry seminar, University of Warwick, United Kingdom January 2019 Colloquium, University of Toronto, Canada January 2019 Colloquium, Yale University, United States November 2018 Algebraic and Tropical Geometry seminar, Yale University, United States November 2018 Conference Equivariant and motivic homotopy theory, Isaac Newton Institute, Cambridge, United Kingdom August 2018 Algebra and Number theory day, Johns Hopkins University, United States April 2018 Arbeitsgemeinschaft: Topological Cyclic Homology, Oberwolfach, Germany April 2018 Algebra and Topology seminar, Université Strasbourg, France January 2018 Colloquium, University of California at Santa Barbara, United States January 2018 Colloquium, University of California at San Diego, United States December 2017 Conference Vector bundles and algebraic curves (VBAC 2017), Essen, Germany (Fourlecture course) September 2017 Mathematische Arbeitstagung 2017 (in honor of Yuri I. Manin's 80th birthday), MaxPlanckInstitut für Mathematik, Bonn, Germany June 2017 Workshop Ktheory in algebraic geometry and number theory, Hausdorff Research Institute for Mathematics, Bonn, Germany May 2017 Conference AlgebroGeometric and Homotopical Methods, Institut MittagLeffler, Sweden March 2017 Colloquium, University of Southern California, United States February 2017 Colloquium, Institut de Mathématiques de Jussieu, Paris, France January 2017 Algebraic Topology seminar, Université Paris 13, France January 2017 Conference Noncommutative, derived and homotopical methods in geometry, Antwerp, Belgium September 2016 International Ktheory Conference, Sydney, Australia August 2016 Conference Interacting Algebraic Geometry, Dijon, France July 2016 Workshop Algebraic Ktheory and motivic cohomology, Oberwolfach, Germany June 2016 Workshop Triangulated Categories and Applications, Banff Institute, Canada June 2016 Geometry, physics, and representation theory seminar, Northeastern University, United States April 2016 Conference MidAtlantic Topology, Johns Hopkins University, United States March 2016 Conference Motives, Tokyo, Japan February 2016 Algebraic Geometry seminar, Università degli Studi di Milano, Italy July 2015 Colloquium, University of California at Los Angeles, United States February 2015 Workshop Cohomological Realizations of Motives, Banff Institute, Canada December 2014 Colloquium, University of Maryland, United States October 2014 Algebra and Number Theory seminar, University of Maryland, United States October 2014 Conference Ktheory and related topics, Beijing, China August 2014 Conference Reimagining the Foundations of Algebraic Topology, MSRI, Berkeley, United States April 2014 Algebraic Geometry seminar, California Institute of Technology, United States January 2014 Colloquium, California Institute of Technology, United States January 2014 Infinite Dimensional Algebraic Geometry seminar, Yale University, United States September 2013 Conference Homotopical methods in algebraic geometry, University of Southern California, United States June 2013 Colloquium, University of California, Berkeley, United States May 2013 Conference Interactions between Noncommutative Algebra and Algebraic Geometry, MSRI, Berkeley, United States April 2013 Conference Motives, Tokyo, Japan December 2012 Conference Algebraic Topology, Arolla, Switzerland August 2012 Conference Periods and Motives, Madrid, Spain July 2012 Conference Noncommutative Algebraic Geometry and its Applications to Physics, Leiden, Netherlands March 2012 Colloquium, California Institute of Technology, United States January 2012 Algebraic Topology seminar, Massachusetts Institute of Technology, United States November 2011 Seminar on Algebra, Geometry and Physics, MaxPlanckInstitut für Mathematik, Germany July 2011 Conference Triangulated categories and applications, Banff Institute, Canada June 2011 Representation Theory seminar, Northeastern University, United States April 2011 Midwest Topology conference, University of Chicago, United States April 2011 Geometric Langlands seminar, University of Chicago, United States April 2011 Noncommutative Geometry seminar, California Institute of Technology, United States March 2011 Noncommutative Algebraic Geometry seminar, Massachusetts Institute of Technology, United States January 2011 Conference Homotopy theory and derived algebraic geometry, Fields Institute, Toronto, Canada August 2010 Conference Topics in Noncommutative Geometry, Buenos Aires, Argentine July 2010 Algebraic Topology seminar, Northwestern University, United States May 2010 Algebraic Topology seminar, University of Illinois at UrbanaChampaign, United States April 2010 Algebraic Topology seminar, University of Chicago, United States April 2010 Algebraic Topology seminar, Massachusetts Institute of Technology, United States March 2010 Algebraic Topology seminar, Stanford University, United States May 2009 Algebra seminar, University of California at Los Angeles, United States May 2009 Conference Cats 3, Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy September 2008 Algebraic Topology seminar, University of Bonn, Germany July 2008 Conference Homotopy Structures in Geometry and Algebra, Centre de Recerca Matemàtica, Barcelona, Spain June 2008 Algebra seminar, Laboratoire J. A. Dieudonné, Nice, France April 2008 
Grothendieck classes of quadrics and involution varieties [link] Conference Noncommutative shapes (in honor of Michel Van den Bergh's 61th birthday) (2022) Antwerp, Belgium Noncommutative Riemann hypothesis [link] Workshop Algebraic cycles, strings and amplitudes (2022) Isaac Newton Institute, Cambridge, United Kingdom Grothendieck classes of quadric hypersurfaces and involution varieties [link] Seminar Quadratic forms, linear algebraic groups and beyond (2022) Noncommutative Riemann hypothesis [link] Noncommutative Geometry and Topology seminar (2021) Czech Academy of Sciences, Prague, Czech Republic Noncommutative Weil conjecture
[link]
NYC Noncommutative geometry seminar (2021) New York, United States Jacques Tits motivic measure [link]
Workshop Noncommutative motives and telescopetype problems (2020) Hausdorff Research Institute for Mathematics, Bonn, Germany Motivic AtiyahSegal completion
theorem [link]
Algebraic topology seminar (2020) University of Warwick, United Kingdom Noncommutative counterparts of celebrated conjectures [link] Summer school Motivic, equivariant, and noncommutative homotopy theory (2020) Institut des Hautes Études Scientifiques, France Grothendieck's standard conjectures via noncommutative algebraic geometry [link] Mathematische Arbeitstagung 2017 (in honor of Yuri I. Manin's 80th birthday) MaxPlanckInstitut für Mathematik, Bonn, Germany Additive invariants of orbifolds [link] Conference Ktheory in algebraic geometry and number theory (2017) Hausdorff Research Institute for Mathematics, Bonn, Germany Noncommutative motives of separable algebras [link] Conference Cohomological realizations of motives (2014) Banff International Research Station for Mathematical Innovation and Discovery, Canada Motives versus noncommutative motives [link] Conference Reimagining the foundations of algebraic topology (2014) Mathematical Sciences Research Institute, Berkeley, United States Noncommutative motives [link] Conference Interactions between noncommutative algebra, representation theory, and algebraic geometry (2013) Mathematical Sciences Research Institute, Berkeley, United States 