The Gysin triangle via localization and 𝐴¹-homotopy invariance

DOI10.1090/tran/6956zbMath1387.14018arXiv1510.04677OpenAlexW2963844460MaRDI QIDQ4588220

Gonçalo Tabuada, Michel Van den Bergh

Publication date: 1 November 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04677

zbMATH Keywords

periodic cyclic homologydg enhancementperfect complexQuillen's localization theoremlocalizing invariant\(\mathbb A^1\) homotopy invariantdifferential graded (dg) categoryGysin trianglemotivic Gysin trianglesnoncommutative algebraic \(K\)-theorynoncommutative graded motivesnoncommutative motivic Gysin triangleQuillen's algebraic \(K\)-theorythe fundamental theorem in homotopy theory

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) (K)-theory and homology; cyclic homology and cohomology (19D55) (Equivariant) Chow groups and rings; motives (14C15) Motivic cohomology; motivic homotopy theory (14F42) Enriched categories (over closed or monoidal categories) (18D20)

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Cites Work

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• \(\mathbb A^1\)-homotopy invariance of algebraic \(K\)-theory with coefficients and du Val singularities
• Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives
• On the motivic spectra representing algebraic cobordism and algebraic \(K\)-theory
• \(\mathbf{A}^1\)-homotopy theory of noncommutative motives
• Modules over motivic cohomology
• Higher \(K\)-theory via universal invariants
• Algebraic cycles and higher K-theory
• \(\mathbb{A}^1\)-homotopy theory
• On the cyclic homology of ringed spaces and schemes
• On the cyclic homology of exact categories
• Smoothness, semi-stability and alterations
• DG quotients of DG categories.
• Motivic decomposition of isotropic projective homogeneous varieties
• Cyclic homology, comodules, and mixed complexes
• Uniqueness of dg enhancements for the derived category of a Grothendieck category
• Some theorems on actions of algebraic groups
• On motivic decompositions arising from the method of Białynicki-Birula
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• A fixed point formula for action of tori on algebraic varieties
• Triangulated Categories
• The fundamental theorem via derived Morita invariance, localization, and ¹-homotopy invariance
• Vanishing of negative -theory in positive characteristic
• Motivic strict ring models for 𝐾-theory
• ℤ[1/p-motivic resolution of singularities]
• Noncommutative Motives
• Levine's motivic comparison theorem revisited
• Notes on Motives in Finite Characteristic
• Uniqueness of enhancement for triangulated categories
• Higher algebraic K-theory: I
• The Grothendieck duality theorem via Bousfield’s techniques and Brown representability
• The connection between the $K$-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
• On the De Rham cohomology of algebraic varieties
• \(\mathbb{A}^1\)-homotopy theory of schemes