Noncommutative motives of Azumaya algebras

DOI10.1017/S147474801400005XzbMath1356.14007arXiv1307.7946OpenAlexW2051611675MaRDI QIDQ4983490

Michel Van den Bergh, Gonçalo Tabuada

Publication date: 27 March 2015

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7946

zbMATH Keywords

cyclic homologyalgebraic \(K\)-theoryAzumaya algebrasnoncommutative motivesnoncommutative algebraic geometrydg categoriesnilinvariance

Mathematics Subject Classification ID

Related Items (21)

Kimura-finiteness of quadric fibrations over smooth curves ⋮ Schur-finiteness (and Bass-finiteness) conjecture for quadric fibrations and families of sextic du Val del Pezzo surfaces ⋮ Additive invariants of orbifolds ⋮ Noncommutative motives of separable algebras ⋮ Equivariant noncommutative motives ⋮ Noncommutative Weil conjecture ⋮ HPD-invariance of the Tate conjecture(s) ⋮ Noncommutative Hodge conjecture ⋮ Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives ⋮ Embeddings of algebras in derived categories of surfaces ⋮ Picard groups, weight structures, and (noncommutative) mixed motives ⋮ Some remarks concerning Voevodsky's nilpotence conjecture ⋮ The derived Picard group of an affine Azumaya algebra ⋮ Embedding of the derived Brauer group into the secondary \(K\)-theory ring ⋮ Noncommutative Riemann hypothesis ⋮ A note on Grothendieck’s standard conjectures of type 𝐶⁺ and 𝐷 in positive characteristic ⋮ Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative \(K3\) surfaces ⋮ Weil restriction of noncommutative motives ⋮ Proper connective differential graded algebras and their geometric realizations ⋮ A note on Grothendieck’s standard conjectures of type $C^+$ and $D$ ⋮ \(\mathbb{A}^1\)-homotopy invariants of dg orbit categories

Cites Work

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• Localization theorems in topological Hochschild homology and topological cyclic homology
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• Higher \(K\)-theory via universal invariants
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• On the cyclic homology of exact categories
• Invariance and localization for cyclic homology of DG algebras
• Théorie de la descente et algèbres d'Azumaya
• Localization of modules for a semisimple Lie algebra in prime characteristic (with an appendix by R. Bezrukavnikov and S. Riche, Computation for \(\text{sl}(3))\)
• Negative \(K\)-theory of derived categories
• Symmetric monoidal structure on non-commutative motives
• Notes on Motives in Finite Characteristic
• Uniqueness of enhancement for triangulated categories
• A semiorthogonal decomposition for Brauer-Severi schemes
• K-Theory of Azumaya Algebras over Schemes
• On Maximally Central Algebras
• Deformation quantization of algebraic varieties.

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