Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky versus Hanamura

DOI10.1017/S147474800800011XzbMath1161.14014arXivmath/0601713MaRDI QIDQ5302649

Mikhail Vladimirovich Bondarko

Publication date: 8 January 2009

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

Full work available at URL: https://arxiv.org/abs/math/0601713

zbMATH Keywords

algebraic cyclesmotivesrealization and cohomologyweight filtrations ansd spectral sequences

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Étale and other Grothendieck topologies and (co)homologies (14F20) Global theory of complex singularities; cohomological properties (32S20) Differential graded algebras and applications (associative algebraic aspects) (16E45) Motivic cohomology; motivic homotopy theory (14F42)

Related Items (28)

Hodge realization of Voevodsky motives ⋮ Exponentiation of motivic measures ⋮ Motivic cohomology, localized Chern classes, and local terms ⋮ NON-COMMUTATIVE LOCALIZATIONS OF ADDITIVE CATEGORIES AND WEIGHT STRUCTURES ⋮ The weight complex functor is symmetric monoidal ⋮ Nearby motives and motivic nearby cycles ⋮ A descent principle for compactly supported extensions of functors ⋮ Tensor Structure on Smooth Motives ⋮ Interactions between algebraic geometry and noncommutative algebra. Abstracts from the workshop held May 1--7, 2022 ⋮ On the mixed Tate property and the motivic class of the classifying stack of a finite group ⋮ On exact categories and applications to triangulated adjoints and model structures ⋮ On weakly negative subcategories, weight structures, and (weakly) approximable triangulated categories ⋮ Feynman integrals and motives of configuration spaces ⋮ Zeta functions in triangulated categories ⋮ Some Observations About Motivic Tensor Triangulated Geometry over a Finite Field ⋮ On Chow-weight homology of motivic complexes and its relation to motivic homology ⋮ Numerical functors on Voevodsky's motives ⋮ Motives of Deligne-Mumford stacks ⋮ \(\mathbb A^1\)-equivalence of zero cycles on surfaces. II ⋮ Weight structures vs.t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general) ⋮ ℤ[1/p-motivic resolution of singularities] ⋮ On Chow weight structures without projectivity and resolution of singularities ⋮ Chow motives without projectivity ⋮ Motivic Springer theory ⋮ Theorem of the heart in negative \(K\)-theory for weight structures ⋮ Mixed motivic sheaves (and weights for them) exist if ‘ordinary’ mixed motives do ⋮ On Chow-weight homology of geometric motives ⋮ On lambda operations on mixed motives

Cites Work

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• Mixed motives and algebraic cycles. II
• Motives, numerical equivalence, and semi-simplicity
• Smoothness, semi-stability and alterations
• DG quotients of DG categories.
• Mixed motives and algebraic cycles. III
• Homological and cohomological motives of algebraic varieties
• An extension criterion for functors defined on smooth schemes
• Mixed motives and algebraic cycles. I
• Homology of schemes
• A DG guide to Voevodsky's motives
• Cycles, Transfers, and Motivic Homology Theories. (AM-143)
• The slice filtration and mixed Tate motives
• Idempotent completion of triangulated categories

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