Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives

DOI10.1016/j.jalgebra.2014.06.028zbMath1310.19002arXiv1310.4063OpenAlexW2963922200MaRDI QIDQ404547

Gonçalo Tabuada

Publication date: 4 September 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.4063

zbMATH Keywords

toric varietiescyclic homologyalgebraic \(K\)-theorytorsorshomogeneous varietiesnoncommutative motivesnoncommutative algebraic geometrytwisted forms

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) (K)-theory and homology; cyclic homology and cohomology (19D55) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) (K)-theory of schemes (19E08) Applications of methods of algebraic (K)-theory in algebraic geometry (14C35) Affine algebraic groups, hyperalgebra constructions (14L17)

Related Items

Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras ⋮ Jacques Tits motivic measure ⋮ Noncommutative motives of separable algebras ⋮ Equivariant noncommutative motives ⋮ Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives ⋮ On nonexistence of full exceptional collections on some relative flags ⋮ Picard groups, weight structures, and (noncommutative) mixed motives ⋮ Toric surfaces over an arbitrary field ⋮ On derived categories of arithmetic toric varieties ⋮ Weil restriction of noncommutative motives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Localization theorems in topological Hochschild homology and topological cyclic homology
• K-theory of twisted Grassmannians
• Higher \(K\)-theory via universal invariants
• Generalized spectral categories, topological Hochschild homology and trace maps
• K-theory of quadric hypersurfaces
• On the derived categories of coherent sheaves on some homogeneous spaces
• On the cyclic homology of ringed spaces and schemes
• On the cyclic homology of exact categories
• \(K\)-theory of algebraic tori and toric varieties
• On the algebraic \(K\)-theory of twisted flag varieties
• Théorie de la descente et algèbres d'Azumaya
• Products, multiplicative Chern characters, and finite coefficients via noncommutative motives
• \(E_n\)-regularity implies \(E_{n-1}\)-regularity
• Negative \(K\)-theory of derived categories
• Séminaire de géométrie algébrique du Bois Marie 1966/67, SGA 6.Dirigé par P. Berthelot, A. Grothendieck et L. Illusie, Avec la collaboration de D. Ferrand, J. P. Jouanolou, O. Jussilia, S. Kleiman, M. Raynaud et J. P. Serre. Théorie des intersections et théorème de Riemann-Roch
• Symmetric monoidal structure on non-commutative motives
• The fundamental theorem via derived Morita invariance, localization, and ¹-homotopy invariance
• Notes on Motives in Finite Characteristic
• Uniqueness of enhancement for triangulated categories
• Higher algebraic K-theory: I
• Noncommutative motives of Azumaya algebras
• A guided tour through the garden of noncommutative motives
• From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives
• Galois descent of additive invariants