Schematic homotopy types and non-abelian Hodge theory

DOI10.1112/S0010437X07003351zbMath1158.14013arXivmath/0107129MaRDI QIDQ3509990

Bertrand Toën, Tony G. Pantev, Ludmil Katzarkov

Publication date: 25 June 2008

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0107129

zbMATH Keywords

rational homotopy theoryhomotopy typefundamental groupssimplicial sheavesHodge theorynon-abelian Hodge theoryGrothendieck topologiescomplex protective varieties

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Étale and other Grothendieck topologies and (co)homologies (14F20) Homotopy theory and fundamental groups in algebraic geometry (14F35) Compact Kähler manifolds: generalizations, classification (32J27) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20)

Related Items (9)

Rational homotopy theory and differential graded category ⋮ \(F\)-isocrystals and homotopy types ⋮ Galois actions on homotopy groups of algebraic varieties ⋮ Real Non-Abelian Mixed Hodge Structures for Quasi-Projective Varieties: Formality and Splitting ⋮ The de Rham homotopy theory and differential graded category ⋮ Compact Kähler manifolds with elliptic homotopy type ⋮ A geometric construction of semistable extensions of crystalline representations ⋮ Towards non–abelian 𝑝–adic Hodge theory in the good reduction case ⋮ Algebraic and topological aspects of the schematization functor

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