Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting

DOI10.1090/memo/1150zbMath1376.14014arXiv1104.1409OpenAlexW2962845908MaRDI QIDQ5365192

Jonathan Paul Pridham

Publication date: 6 October 2017

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

Full work available at URL: https://arxiv.org/abs/1104.1409

zbMATH Keywords

non-abelian Hodge theory

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Variation of Hodge structures (algebro-geometric aspects) (14D07) Homotopy theory and fundamental groups in algebraic geometry (14F35) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Mixed Hodge theory of singular varieties (complex-analytic aspects) (32S35)

Related Items

Rational homotopy theory and differential graded category, Galois actions on homotopy groups of algebraic varieties, Derived moduli of complexes and derived Grassmannians, The de Rham homotopy theory and differential graded category, Techniques of constructions of variations of mixed Hodge structures, Quantisation of derived Lagrangians

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Presenting higher stacks as simplicial schemes
• Real mixed Hodge structures
• Analytic nonabelian Hodge theory
• Variation of mixed Hodge structure. I
• Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures
• Algebraic geometry and analytic geometry
• On homotopy theory and c. s. s. groups
• Unifying derived deformation theories
• The homotopy theory of strong homotopy algebras and bialgebras
• Logarithmic de Rham complexes and vanishing theorems
• The de Rham homotopy theory of complex algebraic varieties. I
• La conjecture de Weil. II
• Hodge cycles, motives, and Shimura varieties
• Calculating simplicial localizations
• On the \(\Gamma\)-factors attached to motives
• Higgs bundles and local systems
• Limits of Hodge structures
• Real homotopy theory of Kähler manifolds
• Infinitesimal computations in topology
• The algebraic topology of smooth algebraic varieties
• The proalgebraic completion of rigid groups.
• Galois actions on homotopy groups of algebraic varieties
• The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
• Affine stacks
• Homotopical algebra
• Rational homotopy theory
• Théorie de Hodge. II. (Hodge theory. II)
• Théorie de Hodge. III
• The Hodge theoretic fundamental group and its cohomology
• Towards non–abelian 𝑝–adic Hodge theory in the good reduction case
• Derived moduli of schemes and sheaves
• Asymptotic behaviour of tame harmonic bundles and an application to pure twistor 𝐷-modules. I
• A model category structure on the category of simplicial categories
• Deforming 𝑙-adic representations of the fundamental group of a smooth variety
• Schematic homotopy types and non-abelian Hodge theory
• Pro-algebraic homotopy types
• Algebraic and topological aspects of the schematization functor
• Weight decompositions on étale fundamental groups
• Mixed Hodge theory for unitary local Systems
• Deformations of representations of fundamental groups of open Kähler manifolds
• Completions of mapping class groups and the cycle $C - C^-$
• Infinitesimal presentations of the Torelli groups
• The Hodge filtration on nonabelian cohomology
• The hodge de rham theory of relative malcev completion1
• On the mixed Hodge structure associated to $\pi_3$ of a simply connected complex projective manifold
• On ℓ-adic Pro-algebraic and Relative Pro-ℓ Fundamental Groups
• Functors of Artin Rings
• Pro-Affine Algebraic Groups
• The deformation theory of representations of fundamental groups of compact Kähler manifolds
• Simplicial homotopy theory
• On the \(\Gamma\)-factors of motives. II