My
publications are available at MathSciNet Motivic concentration theorem with Michel Van den Bergh Mathematical Research Letters, 27 (2020), no. 2, 565-589 Noncommutative motives in positive characteristic and their applications Advances in Mathematics, 349 (2019), 648-681 Vanishing of the negative homotopy K-theory of quotient singularities Journal of the Institute of Mathematics of Jussieu, 18 (2019), no. 3, 619-627 On Grothendieck's standard conjectures of type C and D in positive characteristic Proceedings of the American Mathematical Society 147 (2019), no. 12, 5039-5054 Feynman quadrics-motive of the massive sunset graph with Matilde Marcolli Journal of Number Theory, 195 (2019), 159-183 A note on the Schur-finiteness of linear sections Mathematical Research Letters, 25 (2018), no. 1, 237-253 Invariants of noncommutative projective schemes Moscow Mathematical Journal, 18 (2018), no. 4, 787-797 Noncommutative rigidity Mathematische Zeitschrift, 289 (2018), no. 3, 1281-1298 A note on Grothendieck's standard conjectures of type C and D Proceedings of the American Mathematical Society, 146 (2018), no. 4, 1389-1399 Equivariant noncommutative motives Annals of K-theory, 3 (2018), no. 1, 125-156 Additive invariants of orbifolds with Michel Van den Bergh Geometry and Topology, 22 (2018), 3003-3048 Some remarks concerning Voevodsky's nilpotence conjecture with Marcello Bernardara and Matilde Marcolli Journal für die reine und angewandte Mathematik, 738 (2018), 299-312 The Gysin triangle via localization and A^1-homotopy invariance with Michel Van den Bergh Transactions of the American Mathematical Society, 370 (2018), no. 1, 421-446 Modified mixed realizations, new additive invariants, and periods of dg categories International Mathematics Research Notices, 34 (2017), 7607-7638 A^1-homotopy invariance of algebraic K-theory with coefficients and du Val singularities Annals of K-theory, 2 (2017), no. 1, 1-25 Kimura-finiteness of quadric fibrations over smooth curves C. R. Math. Acad. Sci. Paris, 355 (2017), 628-632 (presented by Christophe Soule) A^1-homotopy invariants of corner skew Laurent polynomial algebras Journal of Noncommutative Geometry 11 (2017), no. 4, 1627-1643 Picard groups, weight structures, and (noncommutative) mixed motives with Mikhail Bondarko Documenta Mathematica 22 (2017), 45-66 Bost-Connes systems, Categorification, Quantum statistical mechanics, and Weil numbers with Matilde Marcolli Journal of Noncommutative Geometry 11 (2017), no. 1, 1-49 A note on secondary K-theory Algebra and Number Theory, 10 (2016), no. 4, 887-906 Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras Selecta Mathematica, 22 (2016), no. 2, 735-764 Algebraic K-theory with coefficients of cyclic quotient singularities C. R. Math. Acad. Sci. Paris, 354 (2016), 449-452 (presented by Michel Duflo) Noncommutative numerical motives, Tannakian structures, and motivic Galois groups with Matilde Marcolli Journal of the European Mathematical Society 18 (2016), 623-655 Noncommutative motives of separable algebras with Michel Van den Bergh Advances in Mathematics, 303 (2016), 1122-1161 K-theory of endomorphisms via noncommutative motives with Andrew J. Blumberg and David Gepner Transactions of the American Mathematical Society 368 (2016), no. 2, 1435-1465 Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) noncommutative motives with Marcello Bernardara Izv. Ross. Akad. Nauk. Ser. Mat. 80 (2016), no. 3, 3-22 A^1-homotopy theory of noncommutative motives Journal of Noncommutative Geometry 9 (2015), no. 3, 851-875 Bivariant cyclic cohomology and Connes' bilinear pairings in noncommutative motives Journal of Noncommutative Geometry 9 (2015), no. 2, 265-285 Exponentiation of motivic measures with Niranjan Ramachandran Journal of the Ramanujan Mathematical Society 30, (2015), no. 4, 349-360 Weil restriction of noncommutative motives Journal of Algebra, 430 (2015), 119-152 A^1-homotopy invariants of dg orbit categories Journal of Algebra, 434 (2015), 169-192 From exceptional collections to motivic decompositions via noncommutative motives with Matilde Marcolli Journal für die reine und angewandte Mathematik 701 (2015), 153-167 Unconditional noncommutative motivic Galois groups with Matilde Marcolli Hodge theory and classical algebraic geometry. Contemporary Mathematics 647 (2015), 109-115 Noncommutative motives of Azumaya algebras with Michel Van den Bergh Journal of the Institute of Mathematics of Jussieu, 14 (2015), no. 2, 379-403 Relations between the Chow motive and the noncommutative motive of a smooth projective variety with Marcello Bernardara Journal of Pure and Applied Algebra, 219 (2015), no. 11, 5068-5077 Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives Advances in Mathematics, 264 (2014), 506-545 Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives Journal of Algebra, 417 (2014), 15-38 A Quillen model for classical Morita theory and a tensor categorification of the Brauer group with Ivo Dell'Ambrogio Journal of Pure and Applied Algebra, 218 (2014), no. 12, 2337-2355 Uniqueness of the multiplicative cyclotomic trace with Andrew J. Blumberg and David Gepner Advances in Mathematics, 260 (2014), 191-232 Jacobians of noncommutative motives with Matilde Marcolli Moscow Mathematical Journal, 14 (2014), no. 3, 577-594 Galois descent of additive invariants Bulletin of the London Mathematical Society, 46 (2014), no. 2, 385-395 E_n-regularity implies E_(n-1)-regularity Documenta Mathematica, 19 (2014), 121-139 Witt vectors and K-theory of automorphisms via noncommutative motives Manuscripta Mathematica, 143 (2014), no. 3-4, 473-482 Noncommutative motives, numerical equivalence, and semi-simplicity with Matilde Marcolli American Journal of Mathematics, 136 (2014), no. 1, 59-75 Noncommutative Artin motives with Matilde Marcolli Selecta Mathematica, 20 (2014), 315-358 Morita homotopy theory of C*-categories with Ivo Dell'Ambrogio Journal of Algebra, 398 (2014), 162-199 Lefschetz and Hirzebruch-Riemann-Roch formulas via noncommutative motives with Denis-Charles Cisinski Journal of Noncommutative Geometry 8 (2014), no. 4, 1171-1190 Chow motives versus noncommutative motives Journal of Noncommutative Geometry 7 (2013), no. 3, 767-786 Fundamental isomorphism conjecture via noncommutative motives with Paul Balmer Mathematische Nachrichten, 286 (2013), no. 8-9, 791-798 A universal characterization of higher algebraic K-theory with Andrew J. Blumberg and David Gepner Geometry and Topology, 17 (2013), 733-838 Weil cohomologies and derived dg categories Journal of Pure and Applied Algebra, 217 (2013), 1294-1302 Products, multiplicative Chern characters, and finite coefficients via noncommutative motives Journal of Pure and Applied Algebra, 217 (2013), 1279-1293 Kontsevich's noncommutative numerical motives with Matilde Marcolli Compositio Mathematica, 148 (2012), 1811-1820 Weight structure on Kontsevich's noncommutative mixed motives Homology, Homotopy and Applications, 14(2) (2012), 129-142 The fundamental theorem via derived Morita invariance, localization, and A^1-homotopy invariance Journal of K-Theory, 9 (2012), no. 3, 407-420 Transfer maps and projection formulas Proceedings of the American Mathematical Society, 140 (2012), 2589-2597 Symmetric monoidal structure on noncommutative motives with Denis-Charles Cisinski Journal of K-Theory, 9 (2012), no. 2, 201-268 Tensor triangular geometry of noncommutative motives with Ivo Dell'Ambrogio Advances in Mathematics, 229 (2012), no. 2, 1329-1357 Co-representability of the Grothendieck group of endomorphisms functor in the category of noncommutative motives Homology, Homotopy and Applications, 13(2) (2011), 315-328 Universal suspension via noncommutative motives Journal of Noncommutative Geometry 5 (2011), no. 4, 573-589 A simple criterion for extending natural transformations to higher K-theory Documenta Mathematica 16 (2011), 657-668 Nonconnective K-theory via universal invariants with Denis-Charles Cisinski Compositio Mathematica 147 (2011), 1281-1320 A universal characterization of the Chern character maps Proceedings of the American Mathematical Society 139 (2011), 1263-1271 On Drinfeld's DG quotient Journal of Algebra, 323 (2010), 1226-1240 Homotopy theory of dg categories via localizing pairs and Drinfeld's DG quotient Homology, Homotopy and Applications, 12(1) (2010), 187-219 Matrix invariants of spectral categories International Mathematics Research Notices, 13 (2010), 2459-2511 Generalized spectral categories, topological Hochschild homology, and trace maps Algebraic and Geometric Topology, 10 (2010), 137-213 Differential graded versus simplicial categories Topology and its Applications, 157 (2010), no. 3, 563-593 Postnikov towers, k-invariants and obstruction theory for dg categories Journal of Algebra, 321 (2009), no. 12, 3850-3877 Homotopy theory of spectral categories Advances in Mathematics, 221 (2009), no. 4, 1122-1143 Noncommutative Andre-Quillen cohomology for differential graded categories Journal of Algebra, 321 (2009), no. 10, 2926-2942 Homotopy theory of well-generated algebraic triangulated categories Journal of K-Theory, 3 (2009), no. 1, 53-75 Higher K-theory via universal invariants Duke Mathematical Journal, 145 (2008), no. 1, 121-206 On the structure of Calabi-Yau categories with a cluster tilting subcategory Documenta Mathematica, 12 (2007), 193-213 Additive invariants of dg categories International Mathematics Research Notices 53 (2005), 3309-3339 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 C. R. Math. Acad. Sci. Paris, 340 (2005), 15-19 (presented by Christophe Soule) (in french) |