2021
DOI: 10.48550/arxiv.2109.14594
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An introduction to derived (algebraic) geometry

Abstract: These are notes from an introductory lecture course on derived geometry, given by the second author, mostly aimed at an audience with backgrounds in geometry and homological algebra. 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 settings.• Footnotes tend to contain details and comments which are tangential to the main thread of the notes; they are excessive in number.• We adhere strictly to the st… Show more

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Cited by 2 publications
(3 citation statements)
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“…For an alternative characterisation of dg dagger spaces and stacks, we can use the approach via Čech nerve-type constructions as in [Pri5] and [EP,§6]. Instead of defining a presheaf O X on a site associated to π 0 X, we can just take a hypercover Z • of π 0 X with each Z n a disjoint union of dagger affinoid spaces U , and then give a dg dagger algebra…”
Section: Definitionsmentioning
confidence: 99%
See 1 more Smart Citation
“…For an alternative characterisation of dg dagger spaces and stacks, we can use the approach via Čech nerve-type constructions as in [Pri5] and [EP,§6]. Instead of defining a presheaf O X on a site associated to π 0 X, we can just take a hypercover Z • of π 0 X with each Z n a disjoint union of dagger affinoid spaces U , and then give a dg dagger algebra…”
Section: Definitionsmentioning
confidence: 99%
“…Alternatively, we could proceed as in [Pri7, §2] and define these structures via Čech nerve-type constructions as in [Pri5] and [EP,§6] . Given a suitable simplicial hypercover Z • of π 0 X, the definitions then reduce to taking cosimplicial homotopy limits, so that…”
Section: Structures On Dagger Dg Spaces and Stacksmentioning
confidence: 99%
“…In this section, we collect some results about dg-schemes and derived schemes. Other than original papers like [5], [37], [34], [24] [18] [36], we also reference some expository notes and textbooks including [35], [10], [31] and [8].…”
Section: Derived Algebraic Geometrymentioning
confidence: 99%