Algebraic and topological aspects of the schematization functor

DOI10.1112/S0010437X09004096zbMath1183.14017arXivmath/0503418MaRDI QIDQ3636890

Bertrand Toën, Ludmil Katzarkov, Tony G. Pantev

Publication date: 30 June 2009

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

Full work available at URL: https://arxiv.org/abs/math/0503418

zbMATH Keywords

fundamental groupsnon-abelian Hodge theoryschematization functoraffine stackscosimplicial \(k\)-algebrascosimplicial Hopf \(k\)-algebrasschematic homotopy types

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Homotopy theory and fundamental groups in algebraic geometry (14F35) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25) Generalizations (algebraic spaces, stacks) (14A20) Coalgebras and comodules; corings (16T15)

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Cites Work

• Homotopical algebraic geometry. I: Topos theory
• Simplicial presheaves
• Exactness properties of profinite completion functors
• Infinitesimal computations in topology
• \(p\)-adic homotopy theory
• Rational and real homotopy theory with arbitrary fundamental groups
• Affine stacks
• Schematic homotopy types and non-abelian Hodge theory
• Pro-algebraic homotopy types
• Algebras and Modules in Monoidal Model Categories
• Sheafifiable homotopy model categories

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