Mixed motives and their realization in derived categories

DOI10.1007/BFb0095503zbMath0938.14008OpenAlexW573663564MaRDI QIDQ1895537

Annette Huber-Klawitter

Publication date: 10 August 1995

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0095503

zbMATH Keywords

derived categorymotivic sheavesmixed Hodge structurede Rham theoryhigher \(K\)-groupsabsolute cohomologiesDeligne cohomologiesmotivic extension group

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) de Rham cohomology and algebraic geometry (14F40) Motivic cohomology; motivic homotopy theory (14F42) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Research exposition (monographs, survey articles) pertaining to (K)-theory (19-02)

Related Items (22)

Dirichlet motives via modular curves ⋮ The Relative (de-)Perfectoidification Functor and Motivic p-Adic Cohomologies ⋮ Hodge realization of Voevodsky motives ⋮ Weight decompositions of Thom spaces of vector bundles in rational homotopy ⋮ Representation stability for families of linear subspace arrangements ⋮ Motivic cohomology ⋮ Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety ⋮ Simplicial descent categories ⋮ Deligne periods of mixed motives, $K$-theory and the entropy of certain $\mathbb {Z}^n$-actions ⋮ Realization of Levine's motives and \(p\)-adic Hodge cohomology ⋮ Groupes fondamentaux motiviques de Tate mixte ⋮ Nori 1-motives ⋮ Syntomic regulators and \(p\)-adic integration. I: Rigid syntomic regulators ⋮ \(\ell\)-adic scalization of geometric triangular motives. II ⋮ Surjectivity of \(p\)-adic regulators on \(K_2\) of Tate curves ⋮ \(\ell\)-adic realization of mixed motives. ⋮ Le complexe motivique de De Rham ⋮ Geometric syntomic cohomology and vector bundles on the Fargues-Fontaine curve ⋮ Generalized Beilinson Elements and Generalized Soulé Characters ⋮ Mixed Hodge complexes on algebraic varieties and \(t\)-structures ⋮ Sheaves of 𝐸-infinity algebras and applications to algebraic varieties and singular spaces ⋮ KAROUBI’S RELATIVE CHERN CHARACTER, THE RIGID SYNTOMIC REGULATOR, AND THE BLOCH–KATO EXPONENTIAL MAP

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