A Step towards Computational Derived Algebraic Geometry: The RepHomology Package For Macaulay2 [PDF]
arXivWe introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representation homology of surfaces (with group coefficients, and analogies with algebra and Lie algebra coefficients), and the representation homology of link complements.
Guanyu Li
arxiv +5 more sources
On line bundles in derived algebraic geometry [PDF]
Annals of K-Theory, 2020 9 pages, comments ...
Toni Annala
openalex +6 more sources
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
openalex +7 more sources
Lie algebras of derivations and affine algebraic geometry over fields of characteristic 0 [PDF]
Mathematische Annalen, 1996 In their article ([15]) Pursell and Shanks have formulated the problem to characterize a manifold by its Lie algebra of all vector fields for the first time. Since then this question has been answered for numerous, different geometric objects: for embedded germs of quasihomogeneous isolated singularities by H.
Thomas Siebert
openalex +3 more sources
"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra [PDF]
arXiv, 2003 We develop homotopical algebraic geometry (see math.AG/0207028) in the special context where the base symmetric monoidal model category is the category S of spectra, i.e. what might be called, after Waldhausen, ``brave new algebraic geometry''. We discuss various model topologies on the model category of commutative algebras in S, the associated ...
Bertrand Toën, Gabriele Vezzosi
arxiv +3 more sources
Algebraic Geometry over model categories (a general approach to derived algebraic geometry)
, 2001 LaTeX,xy-pic, 51 ...
Bertrand Toën, Gabriele Vezzosi
openalex +4 more sources
Ramification and descent in homotopy theory and derived algebraic geometry
, 2021 22 pages, comments ...
John D. Berman
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Brauer groups and étale cohomology in derived algebraic geometry [PDF]
Geometry & Topology, 2014 In this paper, we study Azumaya algebras and Brauer groups in derived algebraic geometry. We establish various fundamental facts about Brauer groups in this setting, and we provide a computational tool, which we use to compute the Brauer group in several examples.
Benjamin Antieau, David Gepner
openalex +7 more sources
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
openalex +5 more sources
Blow-ups and normal bundles in connective and nonconnective derived geometries [PDF]
arXiv, 2023 This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is our proposed globalization of a derived algebraic context, itself a generalization of the theory of simplicial commutative rings.
Ben-Bassat, Oren, Hekking, Jeroen
arxiv +2 more sources