# Derived stack

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In [algebraic geometry](/source/algebraic_geometry), a '''derived stack''' is, roughly, a [stack](/source/stack_(mathematics)) together with a [sheaf of commutative ring spectra](/source/sheaf_of_spectra).<ref>{{harvnb|Mathew|Meier|2013|loc=Definition 2.6.}}</ref> It generalizes a [derived scheme](/source/derived_scheme). Derived stacks are the "spaces" studied in [derived algebraic geometry](/source/derived_algebraic_geometry).<ref name=Vezzosi2011>{{cite journal|last=Vezzosi|first=Gabriele|author-link=Gabriele Vezzosi|title=What is ... a Derived Stack?|journal=[Notices of the American Mathematical Society](/source/Notices_of_the_American_Mathematical_Society)|date=August 2011|volume=58|issue=7|pages=955–958|url=https://www.ams.org/notices/201107/rtx110700955p.pdf|access-date=4 March 2014}}</ref>

== Notes ==
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== References ==
* {{citation | last=Toën | first=Bertrand |author-link=Bertrand Toën| title=Derived Algebraic Geometry | year=2014 | arxiv=1401.1044 }}
* {{citation | last=Toën | first=Bertrand | author-link=Bertrand Toën| title=Higher and derived stacks: a global overview | year=2006 | arxiv=math/0604504  | bibcode=2006math......4504T }}
* {{cite thesis | last=Lurie | first=Jacob |author-link=Jacob Lurie| title=Derived Algebraic Geometry | date=2004 | publisher=Massachusetts Institute of Technology | hdl=1721.1/30144 | url=https://dspace.mit.edu/handle/1721.1/30144 }}
* {{cite journal |last1=Mathew |first1=Akhil |last2=Meier |first2=Lennart |arxiv=1311.0514 |title=Affineness and chromatic homotopy theory |year=2013 |doi=10.1112/jtopol/jtv005 |volume=8 |journal=Journal of Topology |issue=2 |pages=476–528|s2cid=119713516 }}

Category:Stacks (mathematics)
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