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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 31st 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexbrushed up the definition at [[algebraic stack]] following the _Stacks project_ text..

   brushed up the definition at algebraic stack following the Stacks project text..

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 31st 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave added to [[algebraic stack]] the statement how these are equivalent to smooth algebraic groupoids.

   have added to algebraic stack the statement how these are equivalent to smooth algebraic groupoids.

3. • CommentRowNumber3.
   • CommentAuthoradeelkh
   • CommentTimeMar 25th 2015
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexAdded the short notes * [[Anatoly Preygel]], _Algebraic stacks_, Seminar notes: Quantization of Hitchin's integrable system and Hecke eigensheaves, 2009, [pdf](http://www.math.harvard.edu/~gaitsgde/grad_2009/SeminarNotes/Sept15-17(stacks).pdf).

   Added the short notes

   • Anatoly Preygel, Algebraic stacks, Seminar notes: Quantization of Hitchin’s integrable system and Hecke eigensheaves, 2009, pdf.
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 3rd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Angelo Vistoli]], Appendix of: _Intersection theory on algebraic stacks and on their moduli spaces_, Inventiones mathematicae volume 97, pages 613–670 (1989) ([doi:10.1007/BF01388892]( https://doi.org/10.1007/BF01388892)) <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/21">v21</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to

   • Angelo Vistoli, Appendix of: Intersection theory on algebraic stacks and on their moduli spaces, Inventiones mathematicae volume 97, pages 613–670 (1989) (doi:10.1007/BF01388892)

   diff, v21, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeApr 8th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Fredrik Meyer]], *Notes on algebraic stacks* (2013) &lbrack;[pdf](https://fredrikmeyer.net/uio-math/algstacks.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/23">v23</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to:

   • Fredrik Meyer, Notes on algebraic stacks (2013) [pdf]

   diff, v23, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 8th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Martin Olsson]], *Algebraic Spaces and Stacks*, Colloquium Publications **62** (2016) &lbrack;[doi:10.1090/coll/062](https://doi.org/10.1090/coll/062), [ISBN:978-1-4704-2798-6](https://bookstore.ams.org/coll-62)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/23">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/23">v23</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to:

   • Martin Olsson, Algebraic Spaces and Stacks, Colloquium Publications 62 (2016) [doi:10.1090/coll/062, ISBN:978-1-4704-2798-6]

   diff, v23, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 15th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Frank Neumann]], *Algebraic Stacks and Moduli of Vector Bundles*, impa (2011) &lbrack;[pdf](https://impa.br/wp-content/uploads/2017/04/PM_36.pdf), [pdf](https://www.cimat.mx/~luis/seminarios/Pilas-algebraicas/neumann-Stacks.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/24">v24</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to:

   • Frank Neumann, Algebraic Stacks and Moduli of Vector Bundles, impa (2011) [pdf, pdf]

   diff, v24, current

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Michael Groechenig]], *Algebraic Stacks*, Lecture notes (2014) &lbrack;[web](http://individual.utoronto.ca/groechenig/stacks.html), [pdf](http://individual.utoronto.ca/groechenig/stacks.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/25">v25</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to:

   • Michael Groechenig, Algebraic Stacks, Lecture notes (2014) [web, pdf]

   diff, v25, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Daniel Halpern-Leistner]], *Moduli theory*, Lecture notes (2020) &lbrack;[pdf](http://pi.math.cornell.edu/~danielhl/moduli_theory_notes.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/25">v25</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

   added pointer to:

   • Daniel Halpern-Leistner, Moduli theory, Lecture notes (2020) [pdf]

   diff, v25, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * [[Angelo Vistoli]], _Grothendieck topologies, fibered categories and descent theory_ &lbrack;[math.AG/0412512](http://arxiv.org/abs/math/0412512), [MR2223406](http://www.ams.org/mathscinet-getitem?mr=2223406)&rbrack; in: Fantechi et al. (eds.), _Fundamental algebraic geometry. Grothendieck's [[FGA explained]]_, Mathematical Surveys and Monographs __123__, Amer. Math. Soc. (2005) 1-104 &lbrack;[ISBN:978-0-8218-4245-4](https://bookstore.ams.org/surv-123-s), [MR2007f:14001](http://www.ams.org/mathscinet-getitem?mr=2007f:14001)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/26">v26</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

    added pointer to:

    • Angelo Vistoli, Grothendieck topologies, fibered categories and descent theory [math.AG/0412512, MR2223406] in: Fantechi et al. (eds.), Fundamental algebraic geometry. Grothendieck’s FGA explained, Mathematical Surveys and Monographs 123, Amer. Math. Soc. (2005) 1-104 [ISBN:978-0-8218-4245-4, MR2007f:14001]

    diff, v26, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded DOI- and author-links for this item: * [[Gérard Laumon]], [[Laurent Moret-Bailly]], _Champs alg&#233;briques_, Ergebn. der Mathematik und ihrer Grenzgebiete **39**, Springer (2000) &lbrack;[doi:10.1007/978-3-540-24899-6](https://doi.org/10.1007/978-3-540-24899-6)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/26">v26</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

    added DOI- and author-links for this item:

    • Gérard Laumon, Laurent Moret-Bailly, Champs algébriques, Ergebn. der Mathematik und ihrer Grenzgebiete 39, Springer (2000) [doi:10.1007/978-3-540-24899-6]

    diff, v26, current

12. • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to the original articles bt Deligne & Mumford and by Artin, and unified the following lists of reviews/monographs, re-arranging into chronological order <a href="https://ncatlab.org/nlab/revision/diff/algebraic+stack/26">diff</a>, <a href="https://ncatlab.org/nlab/revision/algebraic+stack/26">v26</a>, <a href="https://ncatlab.org/nlab/show/algebraic+stack">current</a>

    added pointer to the original articles bt Deligne & Mumford and by Artin, and unified the following lists of reviews/monographs, re-arranging into chronological order

    diff, v26, current