Note sur les opérations de Grothendieck et la réalisation de Betti

DOI10.1017/S1474748009000127zbMath1202.14018MaRDI QIDQ3552192

Joseph Ayoub

Publication date: 13 April 2010

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

zbMATH Keywords

motivesmodel categoriesGrothendieck's six operationsBetti realizationsvanishing cycles formalism

Mathematics Subject Classification ID

Resolutions; derived functors (category-theoretic aspects) (18G10) Étale and other Grothendieck topologies and (co)homologies (14F20) Classical real and complex (co)homology in algebraic geometry (14F25) Motivic cohomology; motivic homotopy theory (14F42) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Grothendieck topologies and Grothendieck topoi (18F10)

Related Items (30)

Hodge realization of Voevodsky motives ⋮ Perverse, Hodge and motivic realizations of étale motives ⋮ Intermediate extension of Chow motives of abelian type ⋮ Arakelov motivic cohomology II ⋮ Motivic realizations of singularity categories and vanishing cycles ⋮ The Adams-Novikov spectral sequence and Voevodsky's slice tower ⋮ Endoscopic congruences modulo adjoint \(L\)-values for \(\mathrm{GSp}(4)\) ⋮ K$K$‐Motives and Koszul duality ⋮ Tensor structure for Nori motives ⋮ The \(C_2\)-effective spectral sequence for \(C_2\)-equivariant connective real \(K\)-theory ⋮ Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety ⋮ Motives of moduli spaces of bundles on curves via variation of stability and flips ⋮ The universal six-functor formalism ⋮ Nearby motivic sheaves of weighted equivariant functions ⋮ Thick Ideals in Equivariant and Motivic Stable Homotopy Categories ⋮ Some Observations About Motivic Tensor Triangulated Geometry over a Finite Field ⋮ The Berkovich realization for rigid analytic motives ⋮ Triangulated categories of relative 1-motives ⋮ Polylogarithm for families of commutative group schemes ⋮ From motives to comodules over the motivic Hopf algebra ⋮ An isomorphism of motivic Galois groups ⋮ Derived Azumaya algebras and twisted \(K\)-theory ⋮ Motivic periods and Grothendieck arithmetic invariants ⋮ On weight truncations in the motivic setting ⋮ Bivariant theories in motivic stable homotopy ⋮ Betti realization of varieties defined by formal Laurent series ⋮ Artin motives, weights, and motivic nearby sheaves ⋮ RIGIDITY FOR RIGID ANALYTIC MOTIVES ⋮ Supports for constructible systems ⋮ A modification of the Kontsevich-Zagier conjecture on periods

Cites Work

• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Hypercovers and simplicial presheaves
• Mixed Hodge modules
• \(\mathbb{A}^1\)-homotopy theory of schemes
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Note sur les opérations de Grothendieck et la réalisation de Betti