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In `F33f`_`[algebraic geometry`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Algebraic_geometry]`_`f, a `!derived stack`! is, roughly, a `F33f`_`[stack`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Stack_(mathematics)]`_`f together with a `F33f`_`[sheaf of commutative ring spectra`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sheaf_of_spectra]`_`f.`:cite-ref-1[`F5bf`_`[1`#cite-note-1]`_`f] It generalizes a `F33f`_`[derived scheme`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Derived_scheme]`_`f. Derived stacks are the "spaces" studied in `F33f`_`[derived algebraic geometry`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Derived_algebraic_geometry]`_`f.`:cite-ref-vezzosi2011-2-0[`F5bf`_`[2`#cite-note-vezzosi2011-2]`_`f]

>>Contents

• `F0af`_`[Notes`#notes]`_`f

• `F0af`_`[References`#references]`_`f

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>>Notes

`:cite-note-1`!1.`! `F0af`_`[↑`#cite-ref-1]`_`f `F33f`_`[Mathew & Meier 2013`#citerefmathewmeier2013]`_`f, Definition 2.6.

`:cite-note-vezzosi2011-2`!2.`! `F0af`_`[↑`#cite-ref-vezzosi2011-2-0]`_`f `:citerefvezzosi2011`a`F33f`_`[Vezzosi, Gabriele`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Gabriele_Vezzosi]`_`f (August 2011). "What is ... a Derived Stack?" (PDF). `*`F33f`_`[Notices of the American Mathematical Society`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Notices_of_the_American_Mathematical_Society]`_`f`*. `!58`! (7): 955–958. Retrieved 4 March 2014.

>>References

• `:citerefto-n2014`a`F33f`_`[Toën, Bertrand`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bertrand_Toën]`_`f (2014), `*Derived Algebraic Geometry`*, `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:1401.1044

• `:citerefto-n2006`a`F33f`_`[Toën, Bertrand`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bertrand_Toën]`_`f (2006), `*Higher and derived stacks: a global overview`*, `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:math/0604504, `F33f`_`[Bibcode`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bibcode_(identifier)]`_`f:2006math......4504T

• `:citereflurie2004`a`F33f`_`[Lurie, Jacob`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Jacob_Lurie]`_`f (2004). `*Derived Algebraic Geometry`* (Thesis). Massachusetts Institute of Technology. `F33f`_`[hdl`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Hdl_(identifier)]`_`f:1721.1/30144.

• `:citerefmathewmeier2013`aMathew, Akhil; Meier, Lennart (2013). "Affineness and chromatic homotopy theory". `*Journal of Topology`*. `!8`! (2): 476–528. `F33f`_`[arXiv`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=ArXiv_(identifier)]`_`f:1311.0514. `F33f`_`[doi`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Doi_(identifier)]`_`f:10.1112/jtopol/jtv005. `F33f`_`[S2CID`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=S2CID_(identifier)]`_`f 119713516.

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