Results 1 to 10 of about 722,703 (184)
Derived Algebraic Geometry [PDF]
arXiv, 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.
Bertrand Toën
arxiv +13 more sources
Notes on derived algebraic geometry [PDF]
arXiv, 2022 These are notes on derived algebraic geometry in the context of animated rings. More precisely, we recall the proof of To\"en-Vaqui\'e that the derived stack of perfect complexes is locally geometric in the language of $\infty$-categories. Along the way, we recall the necessary notions in derived commutative algebra and derived algebraic geometry.
Can Yaylali
arxiv +6 more sources
An introduction to derived (algebraic) geometry [PDF]
arXiv, 2021 Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly in characteristic $0$, but we also see the tweaks which extend most of the content to analytic and differential ...
J. Eugster, J. P. Pridham
arxiv +6 more sources
Derived Algebraic Geometry VI: E_k Algebras [PDF]
arXiv, 2009 In this paper, we study algebras over the little cubes operads introduced by Boardman and Vogt, using the formalism of higher category theory.
Jacob Lurie
arxiv +5 more sources
Morphisms in Derived Algebraic Geometry [PDF]
arXivWe give a characterization of morphisms in derived algebraic geometry in the more general context of morphisms in spectral algebraic geometry. Using this characterization, we prove two versions of Tannaka duality and the formal GAGA principle in the setting of derived algebraic geometry.
Chang‐Yeon Chough
arxiv +5 more sources
A note on the cotangent complex in derived algebraic geometry [PDF]
arXiv, 2010 This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting for deformation and obstruction theories.
Gabriele Vezzosi
arxiv +5 more sources
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 ...
Bertrand Toën
core +6 more sources
Motivic model categories and motivic derived algebraic geometry [PDF]
arXiv, 2017 In this paper, we develop an enhancement of derived algebraic geometry to apply to $\mathbb{A}^1$-homotopy theory introduced by Morel and Voevodsky. We call the enhancement "motivic derived algebraic geometry". We shall actually formulate "motivic" versions of $\infty$-categories, $\infty$-topoi, spectral schemes and spectral Deligne--Mumford stacks ...
Yuki Kato
arxiv +5 more sources
Geometric Langlands twists of $N=4$ gauge theory from derived algebraic geometry [PDF]
Advances in Theoretical and Mathematical Physics, 2018 We develop techniques for describing the derived moduli spaces of solutions to the equations of motion in twists of supersymmetric gauge theories as derived algebraic stacks. We introduce a holomorphic twist of N=4 supersymmetric gauge theory and compute
Chris Elliott, Philsang Yoo
core +7 more sources
Good Moduli Spaces in Derived Algebraic Geometry
, 2023 We develop a theory of good moduli spaces for derived Artin stacks, which naturally generalizes the classical theory of good moduli spaces introduced by Alper.
Eric Ahlqvist +3 more
core +5 more sources