Chow motives versus noncommutative motives

DOI10.4171/JNCG/134zbMath1296.14019arXiv1103.0200MaRDI QIDQ380276

Gonçalo Tabuada

Publication date: 13 November 2013

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.0200

zbMATH Keywords

motivic zeta functionsChow motivesnoncommutative motivesmotivic measuresKimura and Schur finiteness

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Étale cohomology, higher regulators, zeta and (L)-functions ((K)-theoretic aspects) (19F27) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15)

Related Items (20)

Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras ⋮ Integral Chow motives of threefolds with $K$-motives of unit type ⋮ Weil cohomologies and derived dg categories ⋮ Exponentiation of motivic measures ⋮ Noncommutative motives of separable algebras ⋮ Equivariant noncommutative motives ⋮ Voevodsky's mixed motives versus Kontsevich's noncommutative mixed motives ⋮ Noncommutative Hodge conjecture ⋮ Derived categories of centrally‐symmetric smooth toric Fano varieties ⋮ Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties ⋮ On nonexistence of full exceptional collections on some relative flags ⋮ \(q\)-deformations of statistical mechanical systems and motives over finite fields ⋮ Noncommutative Artin motives ⋮ \(K\)-theory and the bridge from motives to noncommutative motives ⋮ Noncommutative counterparts of celebrated conjectures ⋮ Zeta functions, Grothendieck groups, and the Witt ring ⋮ Some remarks concerning Voevodsky's nilpotence conjecture ⋮ Bost-Connes systems, categorification, quantum statistical mechanics, and Weil numbers ⋮ Weil restriction of noncommutative motives ⋮ Relations between the Chow motive and the noncommutative motive of a smooth projective variety

Cites Work

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• Spectra, spectra, spectra -- tensor triangular spectra versus Zariski spectra of endomorphism rings
• Nilpotence, radicals and monoidal structures. With an appendix by Peter O'Sullivan.
• An introduction to motivic zeta functions of motives
• Idempotent completion of triangulated categories

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