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Derived Algebraic Geometry [PDF]
EMS Surveys in Mathematical Sciences, 2014 This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.Comment: Final version.
Bertrand Toën
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Algebraic foliations and derived geometry: the Riemann–Hilbert correspondence [PDF]
Selecta Mathematica, 2022 AbstractThis is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic varieties and on their associated formal and analytic versions.
Bertrand Toën, Gabriele Vezzosi
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Derived Algebraic Geometry III: Commutative Algebra [PDF]
, 2007 This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
Jacob Lurie
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Tannakization in derived algebraic geometry [PDF]
Journal of K-theory, 2014 AbstractIn this paper we begin studying tannakian constructions in ∞-categories and combine them with the theory of motivic categories developed by Hanamura, Levine, and Voevodsky. This paper is the first in a series of papers. For the purposes above, we first construct a derived affine group scheme and its representation category from a symmetric ...
Isamu Iwanari
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Algebraic Geometry over model categories (a general approach to derived algebraic geometry) [PDF]
, 2001 LaTeX,xy-pic, 51 ...
Bertrand Toën, Gabriele Vezzosi
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Graded algebras, projective spectra and blow-ups in derived algebraic\n geometry [PDF]
, 2021 60 pages.
Jeroen Hekking
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Chern character, loop spaces and derived algebraic geometry. [PDF]
, 2009 International audienceIn this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of ...
A Neeman +8 more
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In contemporary mathematics, algebra and geometry intertwine in diverse and subtle ways. This paper distinguishes two fundamentally different modes of algebra--geometry relations: constitutive and representational. In algebraic geometry (AG), the algebraic structure is constitutive of the geometric object: the geometry exists as an intrinsic ...
Sulin, Zhang
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Motifs in Derived Algebraic Geometry [PDF]
, 2015 We formalize the concept of sheaves of sets on a model site by considering variables thereof, or motifs, and we construct functorially defined derived algebraic stacks from them, thereby eliminating the necessity to choose derived extensions.
Renaud Gauthier
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Derived Algebraic Geometry and Deformation Quantization [PDF]
, 2014 This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the construction ...
Toen, Bertrand
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