derived stack

In algebraic geometry, a derived stack is, roughly, a stack together with a sheaf of commutative ring spectra.{{harvnb|Mathew|Meier|2013|loc=Definition 2.6.}} It generalizes a derived scheme. Derived stacks are the "spaces" studied in derived algebraic geometry.{{cite journal|last=Vezzosi|first=Gabriele|author-link=Gabriele Vezzosi|title=What is ... a Derived Stack?|journal=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}}

Notes

{{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 }}