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Algebraic stack — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Algebraic_stack
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-08T10:29:59.228Z
SHA-256 of the archived text: 3c8e4cc5e095f0f5338e7076b47b3176734360b5d67af0c023816b6c5d1134bf
Stable URL of this page: https://metraipolis.com/documento/dc_565bb151f9da

How to cite

Algebraic stack — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Algebraic_stack (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_565bb151f9da (Metraipolis archive dc_565bb151f9da, sha256 3c8e4cc5e095f0f5338e7076b47b3176734360b5d67af0c023816b6c5d1134bf)

BibTeX

@misc{dc565bb151f9da,
  title = {Algebraic stack — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Algebraic_stack},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_565bb151f9da; sha256 3c8e4cc5e095f0f5338e7076b47b3176734360b5d67af0c023816b6c5d1134bf},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Algebraic_stack. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves ℳg,n and the moduli stack of elliptic curves. Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. After Grothendieck developed the general theory of descent, and Giraud the general theory of stacks, the notion of algebraic stacks was defined by Michael Artin.

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Algebraic stack» — https://en.wikipedia.org/wiki/Algebraic_stack
Wikidata Q1687845: «stack in groupoids over the étale site of schemes such that the diagonal map is representable and that there exists a smooth surjection from a scheme» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1687845
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Algebraic_stack?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374366484, consultata il 2026-11-08T10:25:38.995Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d85755612478a5ae2212bb7dcc9d645388b3687d194015e735df94d861835b97