Higher and derived stacks: a global overview

Higher and derived stacks: a global overview (2005)

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by Bertrand Toën

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@MISC{Toën05higherand,
    author = {Bertrand Toën},
    title = {Higher and derived stacks: a global overview },
    year = {2005}
}

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Abstract

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being exhaustive but is intended to cover a rather large part of the subject, starting from the motivations and the foundational material, passing through some examples and basic notions, and ending with some more recent developments and open questions.

Citations

196	Fantechi Intrinsic normal cone - Behrend, B - 1997
140	Complexe cotangent et déformations. I - Illusie - 1971
122	Model categories. Mathematical Surveys and Monographs, 63 - Hovey - 1999
96	Simplicial presheaves - Jardine - 1987
82	A holomorphic Casson invariant for Calabi-Yau 3-folds and bundles on K3 fibrations - Thomas
62	Generators and representability of functors in commutative and non-commutative geometry, Mosc - Bondal, Bergh
51	Simplicial localization of categories - Dwyer, Kan - 1980
51	Higher operads, higher categories - Leinster - 2004
46	Function complexes in homotopical algebra, Topology 19 - Dwyer, Kan - 1980
45	The homotopy theory of dg-categories and derived Morita theory - Toën - 2007
42	The Hodge filtration on nonabelian cohomology ’ alg-geom /9604005 - Simpson
35	Three models for the homotopy theory of homotopy theories, Preprint math.AT/0504334 - Bergner
28	Hypercovers and simplicial presheaves - Dugger, Hollander, et al.
27	A remark on K-theory and S-categories - Toën, Vezzosi
25	Schematic homotopy types and non-abelian Hodge theory, preprint math.AG/0107129 - Katzarkov, Pantev, et al.
23	Segal topoi and stacks over Segal categories, December 25, 2002, to appear - Toën, Vezzosi
21	Une structure de catégorie de modèles de Quillen sur la catégorie des dgcatégories, Comptes Rendus de l’Académie de Sciences de Paris - Tabuada - 2005
21	Homotopical algebraic geometry I: Topos theory - Toën, Vezzosi - 2005
20	Moduli of complexes on a proper morphism - Lieblich
17	Model category structures on chain complexes of sheaves - Hovey
17	Transformation de Fourier generalisée, Preprint alg-geom/9603004 - Laumon
16	Stacks and the homotopy theory of simplicial sheaves, in Equivariant stable homotopy theory and related areas - Jardine - 2000
15	Homotopical and higher categorical structures in algebraic geometry, Hablitation Thesis available at math.AG/0312262 45 - Toën
14	Homotopy over the complex numbers and generalized de Rham cohomology. Moduli of Vector Bundles - Simpson - 1996
13	Derived Hall Algebras - Toen
11	Champs algébriques, A Series of Modern Surveys in Mathematics vol. 39, Springer-Verlag 2000. 59 A. Lazarev, Homotopy theory of A∞ ring spectra and applications to MU-modules - Laumon, Moret-Bailly
8	Derived Quot schemes Ann - Ciocan-Fontanine, Kapranov
8	Descente pour les n-champs, Preprint math.AG/9807049 - Hirschowitz, Simpson
8	A survey of definitions of n-category, Theory and - Leinster
7	Catégories enrichies faibles, Thèse, Université de Nice-Sophia Antipolis - Pellissier - 2002
6	Derived l-adic categories for algebraic stacks - Behrend
6	Images directes cohomologiques dans les catgories de modles - Cisinski
6	A Giraud-type characterisation of the simplicial categories associated to closed model categories as ∞-pretopoi, Preprint math.AT/9903167 - Simpson
6	From HAG to DAG: derived moduli stacks, in Axiomatic, enriched and motivic homotopy theory - Toën, Vezzosi - 2004
5	Non-abelian mixed Hodge structures, preprint math.AG/0006213 - Katzarkov, Pantev, et al.
5	Deformation theory of abelian categories - Lowen, Bergh
5	On ∞-topoi, Preprint math.CT/0306109 - Lurie
5	Champs affines - Toën
5	Moduli of objects in dg-categories, preprint math.AG/0503269 - Toën, Vaquié
4	A homotopy theory for stacks, preprint math.AT/0110247 - Hollander
4	The six operations for sheaves on Artin stacks I: Finite Coefficients, Preprint math.AG/0512097 - Laszlo, Olsson
4	Towards non–abelian P–adic Hodge theory in the good reduction case, Preprint available at http://www.ma.utexas.edu∼molsson - Olsson
2	On Ringel-Hall algebras, in Representations of finite dimensional algebras and related topics in Lie theory and geometry - Deng, Xiao - 2004
2	Riemann-Roch for algebraic stacks III: Virtual structure sheaves and virtual fundamental classes, preprint available at http://www.math.ohio-state.edu∼joshua/pub.html - Joshua
2	Extended deformation functors, Int - Manetti
2	Algebraic n-stacks, preprint math.AG/9609014 - Simpson
1	A characterization of fibrant Segal categories, Preprint math.AT/0603400 - Bergner
1	Representability of the derived Quot functor, thesis - Gorski
1	Pursuing stacks, unpublished manuscript. 48 V. Hinich, Formal stacks as dg-coalgebras - Grothendieck
1	Derived algebraic geometry, thesis, available at the author’s home - Lurie