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searching for Stacks Project 84 found (110 total)

Algebraic stack (3,767 words) [view diff] case mismatch in snippet view article find links to article

presentation—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-08-29. "Section 34.7 (021L): The fppf topology—The Stacks project". stacks.math

Deligne–Mumford stack (1,545 words) [view diff] exact match in snippet view article find links to article

Quotient stack Stacky curve "Deligne–Mumford stacks", The Stacks project, The Stacks Project Authors Deligne, Pierre; Mumford, David (1969), "The irreducibility

Serre duality (3,295 words) [view diff] exact match in snippet view article find links to article

5; Stacks Project, Tag 0A9X. Hartshorne (1977), Theorem III.7.11; Stacks Project, Tag 0BQZ. Hartshorne (1966), Corollary VII.3.4(c); Stacks Project, Tag

Coherent sheaf (6,934 words) [view diff] exact match in snippet view article find links to article

stack Mumford 1999, Ch. III, § 1, Theorem-Definition 3. Stacks Project, Tag 01LA. Stacks Project, Tag 01BU. Serre 1955, §13 Grothendieck & Dieudonné 1960

Fiber product of schemes (1,178 words) [view diff] exact match in snippet view article find links to article

Stacks Project, Tag 020D. Grothendieck, EGA I, Théorème 3.2.6; Hartshorne (1977), Theorem II.3.3. Hartshorne (1977), section II.3. Stacks Project, Tag

Ample line bundle (6,874 words) [view diff] exact match in snippet view article find links to article

Stacks project" Stacks Project, Tag 01AM Stacks Project, Tag 01PS Stacks Project, Tag 01QE Stacks Project, Tag 01VU Stacks Project, Tag 02NP Stacks Project

Hyperconnected space (1,809 words) [view diff] case mismatch in snippet view article find links to article

(004V)—The Stacks project". "Lemma 5.8.3 (004W)—The Stacks project". "Section 5.9 (0050): Noetherian topological spaces—The Stacks project". Hart, Klaas

Divisor (algebraic geometry) (6,617 words) [view diff] exact match in snippet view article

cone, above. Dieudonné (1985), section VI.6. Stacks Project, Tag 00PF. Stacks Project, Tag 02MC. Stacks Project, Tag 02MD. Kollár (2013), Notation 1.2. Hartshorne

Noetherian scheme (1,308 words) [view diff] case mismatch in snippet view article find links to article

"Lemma 28.5.7 (0BA8)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-07-24. "Lemma 28.5.8 (01P0)—The Stacks project". stacks.math.columbia

Irreducible ring (564 words) [view diff] case mismatch in snippet view article find links to article

irreducible scheme.[citation needed] The Stacks project, Tag 02D4 The Stacks project, Tag 01OK The Stacks project, Tag 01ON The Stacks project, Tag 01J2

Torsion-free module (597 words) [view diff] exact match in snippet view article find links to article

Torsion-free modules, The University of Chicago Press, Chicago-London, ISBN 978-0-226-51074-3, MR 0344237 The Stacks Project Authors, The Stacks Project

Coherent sheaf cohomology (4,664 words) [view diff] exact match in snippet view article find links to article

exists. (Hartshorne 1977, (III.1.1A) and section III.2.) Stacks Project, Tag 01X8. Stacks Project, Tag 01XE. (Hartshorne 1977, Theorem III.5.1.) (Hartshorne

Support of a module (905 words) [view diff] exact match in snippet view article find links to article

algébrique 0I, 1.7.1. The Stacks Project authors (2017). Stacks Project, Tag 01B4. The Stacks Project authors (2017). Stacks Project, Tag 01AS. Eisenbud, David

Tor functor (2,163 words) [view diff] exact match in snippet view article find links to article

"History of homological algebra", History of topology (PDF), Amsterdam: North-Holland, pp. 797–836, MR 1721123 The Stacks Project Authors, The Stacks Project

Gorenstein scheme (679 words) [view diff] exact match in snippet view article find links to article

Birational Geometry of Algebraic Varieties, Cambridge University Press, ISBN 0-521-63277-3, MR 1658959 The Stacks Project Authors, The Stacks Project

Irreducible component (951 words) [view diff] case mismatch in snippet view article find links to article

(004U): Irreducible components—The Stacks project". "Section 5.8 (004U): Irreducible components—The Stacks project". This article incorporates material

Length of a module (2,157 words) [view diff] case mismatch in snippet view article find links to article

2013-03-02. Retrieved 2020-05-22. Alt URL "Lemma 10.51.2 (02LZ)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-22. Fulton, William, 1939-

Grothendieck category (2,723 words) [view diff] exact match in snippet view article find links to article

arXiv:1411.0331, doi:10.1007/s00029-016-0263-9, MR 3624905 Stacks Project, Tag 077P; Stacks Project, Tag 0781. Faith, Carl (1973). Algebra: Rings, Modules

Cohen structure theorem (371 words) [view diff] exact match in snippet view article find links to article

local ring. All this material is developed carefully in the Stacks Project "Stacks Project — Tag 0323". stacks.math.columbia.edu. Retrieved 2018-08-13

Direct image functor (1,035 words) [view diff] case mismatch in snippet view article find links to article

modules—The Stacks project". stacks.math.columbia.edu. Retrieved 2022-09-20. "Section 48.3 (0A9D): Right adjoint of pushforward—The Stacks project". stacks

Normal crossing singularity (1,385 words) [view diff] exact match in snippet view article find links to article

Geometry (2 vols.), Berlin: Springer-Verlag, doi:10.1007/978-3-642-18808-4, ISBN 3-540-22533-1, MR 2095471 The Stacks Project Authors, The Stacks Project

Scheme (mathematics) (7,140 words) [view diff] exact match in snippet view article

David Mumford, Can one explain schemes to biologists? The Stacks Project Authors, The Stacks Project https://quomodocumque.wordpress.com/2012/09/03/mochizuki-on-abc/

Completion of a ring (1,627 words) [view diff] exact match in snippet view article find links to article

topology Quasi-unmixed ring "Stacks Project — Tag 05GG". stacks.math.columbia.edu. Retrieved 2025-05-14. "Stacks Project — Tag 0316". stacks.math.columbia

Grothendieck existence theorem (325 words) [view diff] exact match in snippet view article find links to article

1090/CONM/388. ISBN 9780821837191. The Stacks Project authors. "30.24 Grothendieck's existence theorem, I". The Stacks Project authors. "75.42 Grothendieck's

Excellent ring (1,468 words) [view diff] case mismatch in snippet view article find links to article

G-rings—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-07-24. "Section 15.46 (07P6): The singular locus—The Stacks project". stacks.math

Dimension of a scheme (1,249 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-387-90244-9, MR 0463157 The Stacks Project authors. "28 Properties of Schemes/28.10 Dimension". The Stacks Project authors. "29.29 Morphisms of given

Stalk (sheaf) (1,588 words) [view diff] exact match in snippet view article

1017/CBO9780511661761. ISBN 9780521207843. stalk in nLab The Stacks Project authors. "6.11 Stalks". The Stacks Project authors. "6.27 Skyscraper sheaves and stalks"

Triangulated category (5,798 words) [view diff] exact match in snippet view article find links to article

(1994), Definition 10.2.6. Neeman (2001), Remark D.1.5. Stacks Project, Tag 09IS, Stacks Project, Tag 09M1. Neeman (2001), Lemma D.1.3. Neeman (1996), Theorems

Quotient of an abelian category (1,653 words) [view diff] exact match in snippet view article find links to article

{A/B}})\to 0} Section 12.10 The Stacks Project "109.76 The category of modules modulo torsion modules". The Stacks Project. Gabriel, Pierre, Des categories

Gerbe (3,507 words) [view diff] case mismatch in snippet view article find links to article

target—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-10-27. "Section 21.11 (0CJZ): Second cohomology and gerbes—The Stacks project". stacks

Descent (mathematics) (929 words) [view diff] exact match in snippet view article

flat descent Monadic descent Descent data for quasi-coherent sheaves, Stacks Project SGA 1, Ch VIII – this is the main reference Siegfried Bosch; Werner

University of Florida Digital Collections (759 words) [view diff] exact match in snippet view article find links to article

Judaica Digital Collections Natural Sciences Digital Collection Open Stacks Project Performing Arts Digital Collection Psychological Study of the Arts Digital

Semi-continuity (6,680 words) [view diff] exact match in snippet view article find links to article

1007/bf02684890. MR 0163911. "Stacks Project — Lemma 37.30.4". Stacks.math.columbia.edu. Retrieved 2025-04-27. "Stacks Project — Lemma 37.30.5". Stacks.math

Finite morphism (855 words) [view diff] exact match in snippet view article find links to article

Shafarevich 2013, p. 62, Def. 1.2. Hartshorne 1977, Section II.3. Stacks Project, Tag 01WG. Grothendieck, EGA IV, Part 4, Corollaire 18.12.4. Grothendieck

Fundamental theorem of Galois theory (3,178 words) [view diff] exact match in snippet view article find links to article

theory at PlanetMath. The Stacks Project authors. "Theorem 9.21.7 (Fundamental theorem of Galois theory)". The Stacks Project authors. "Theorem 9.22.4

Overcategory (745 words) [view diff] case mismatch in snippet view article find links to article

09375 [math.CT]. "Section 4.32 (02XG): Categories over categories—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-10-16. Lurie, Jacob (2008-07-31)

Constructible topology (260 words) [view diff] case mismatch in snippet view article find links to article

authors prefer the term quasicompact here. "Lemma 5.23.8 (0905)—The Stacks project". stacks.math.columbia.edu. Retrieved 2022-09-20. "Reconciling two different

Perfect complex (562 words) [view diff] case mismatch in snippet view article find links to article

alternative definition of pseudo-coherent complex". MathOverflow. "15.74 Perfect complexes". The Stacks project. "perfect module". ncatlab.org. v t e

Koszul complex (5,545 words) [view diff] exact match in snippet view article find links to article

needed] Koszul–Tate complex Syzygy (mathematics) The Stacks Project, section 0601 The Stacks Project, section 0601, Lemma 15.28.12 Indeed, by linearity

Valuative criterion (289 words) [view diff] exact match in snippet view article find links to article

discrete valuation ring. EGA II, proposition 7.2.3 and théorème 7.3.8. Stacks Project, tags 01KA, 01KY, and 0BX4. Grothendieck, Alexandre; Jean Dieudonné

Injective function (2,635 words) [view diff] case mismatch in snippet view article find links to article

"Section 7.3 (00V5): Injective and surjective maps of presheaves". The Stacks project. Retrieved 2019-12-07. Farlow, S. J. "Section 4.2 Injections, Surjections

Godement resolution (577 words) [view diff] exact match in snippet view article find links to article

doi:10.1017/CBO9781139644136, ISBN 978-0-521-55987-4, MR 1269324 The Stacks Project authors. "20.30 Godement resolution". Goresky, Mark. "Introduction to

Cotangent complex (4,727 words) [view diff] case mismatch in snippet view article find links to article

(08UX): Deformations of ringed spaces and the cotangent complex—The Stacks project". stacks.math.columbia.edu. Retrieved 2021-12-02. "Section 91.23 (08V3):

Approximation property (ring theory) (206 words) [view diff] exact match in snippet view article

1216/rmjm/1181071964. JSTOR 44238106. "Tag 07BW: Smoothing Ring Maps". The Stacks Project. Columbia University, Department of Mathematics. Retrieved 2018-02-19

Galois group (3,237 words) [view diff] case mismatch in snippet view article find links to article

Exchange. Retrieved 2020-11-11. "9.22 Infinite Galois theory". The Stacks project. Milne. "Field Theory" (PDF). p. 98. Archived (PDF) from the original

Invariant basis number (1,027 words) [view diff] exact match in snippet view article find links to article

generating number) must have invariant basis number. (Lam 1999, p. 3) "Stacks Project, Tag 0FJ7". stacks.math.columbia.edu. Retrieved 4 March 2023. (Hungerford

Zero divisor (1,841 words) [view diff] exact match in snippet view article find links to article

Algebra I. Springer Science+Business Media. p. 15. "Non zero-divisors | Stacks Project Blog". 2012-05-10. Retrieved 2025-07-20. Reid, Miles (1995). Undergraduate

Kähler differential (4,390 words) [view diff] exact match in snippet view article find links to article

an enhancement of the de Rham complex for the ring of Witt vectors. "Stacks Project". Retrieved 2022-11-21. Hartshorne (1977, p. 172) Laurent-Gengoux, C

Direct image with compact support (435 words) [view diff] case mismatch in snippet view article find links to article

zero functor. "Section 5.17 (005M): Characterizing proper maps—The Stacks project". stacks.math.columbia.edu. Retrieved 2022-09-25. Schnürer, Olaf M.;

Regular local ring (1,922 words) [view diff] exact match in snippet view article find links to article

ISBN 978-1-4612-0525-8. Chap.5.G. Jean-Pierre Serre, Local algebra, Springer-Verlag, 2000, ISBN 3-540-66641-9. Chap.IV.D. Regular rings at The Stacks Project

Algebraic space (1,594 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-3-540-05496-2, MR 0302647 Danilov, V.I. (2001) [1994], "Algebraic space", Encyclopedia of Mathematics, EMS Press Algebraic space in the stacks project

Formally smooth map (620 words) [view diff] case mismatch in snippet view article find links to article

MR 0238860. "Lemma 37.11.7 (02H6): Infinitesimal lifting criterion—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-04-07. Formally smooth with

Connected space (4,110 words) [view diff] exact match in snippet view article find links to article

CITEREFBredon2013 (help) "5.12 Quasi-compact spaces and maps". The Stacks Project. Columbia University. Archived from the original on 17 March 2025. Retrieved

Projective module (3,092 words) [view diff] case mismatch in snippet view article find links to article

(help) "Section 10.95 (05A4): Descending properties of modules—The Stacks project". stacks.math.columbia.edu. Retrieved 2022-11-03. Exercises 4.11 and

Local cohomology (4,306 words) [view diff] case mismatch in snippet view article find links to article

"Lemma 15.28.6 (0663)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-01. "Lemma 15.28.13 (0913)—The Stacks project". stacks.math.columbia

Annihilator (ring theory) (2,187 words) [view diff] case mismatch in snippet view article

Lemma b, item (i). Eisenbud 2004, p. 67. "Lemma 10.39.5 (00L2)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-13. Anderson & Fuller

Sheaf of algebras (906 words) [view diff] exact match in snippet view article find links to article

EGA 1971, Ch. I, Théorème 9.1.4. EGA 1971, Ch. I, Definition 9.1.1. Stacks Project, Tag 01S5. EGA 1971, Ch. I, Proposition 9.1.5. EGA 1971, Ch. I, Théorème

Jacobson radical (2,927 words) [view diff] case mismatch in snippet view article find links to article

the result. "Section 10.18 (0AMD): The Jacobson radical of a ring—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-12-24. Isaacs 1994, p. 182

ℓ-adic sheaf (1,107 words) [view diff] exact match in snippet view article find links to article

(PMS-33). Princeton University Press. p. 163. ISBN 978-0-691-08238-7. "Stacks Project, Tag 03UL".. Bhatt, Bhargav; Scholze, Peter (2013-09-04). "The pro-étale

Moduli space (4,154 words) [view diff] case mismatch in snippet view article find links to article

Curves: Classical and Tropical" (PDF). AMS. "Lemma 27.13.1 (01NE)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-09-12. "algebraic geometry

Restricted power series (1,377 words) [view diff] exact match in snippet view article find links to article

, φ ( H ) = h {\displaystyle F=GH,\,\varphi (G)=g,\varphi (H)=h} . Stacks Project, Tag 0AKZ. Grothendieck & Dieudonné 1960, Ch. 0, § 7.5.1. Bourbaki 2006

Hirzebruch surface (1,691 words) [view diff] case mismatch in snippet view article find links to article

27.20 (02NB): Twisting by invertible sheaves and relative Proj—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-23. Cox, David A.; Little

Bijection, injection and surjection (2,207 words) [view diff] case mismatch in snippet view article find links to article

"Section 7.3 (00V5): Injective and surjective maps of presheaves—The Stacks project". stacks.math.columbia.edu. Retrieved 2019-12-07. "Earliest Known Uses

Algebraic geometry (7,525 words) [view diff] exact match in snippet view article find links to article

Wisconsin–Milwaukee. Archived from the original on 2021-11-22 – via YouTube. The Stacks Project, an open source textbook and reference work on algebraic stacks and

Nisnevich topology (1,767 words) [view diff] case mismatch in snippet view article find links to article

"Section 10.154 (0BSK): Henselization and strict henselization—The Stacks project". stacks.math.columbia.edu. Retrieved 2021-01-25. "counterexamples -

Cohen–Macaulay ring (3,123 words) [view diff] case mismatch in snippet view article find links to article

archived (PDF) from the original on 5 Mar 2020 "Lemma 31.4.4 (0BXG)—The Stacks project", stacks.math.columbia.edu, retrieved 2020-03-05 Wiegand, Roger (December

Fpqc morphism (371 words) [view diff] exact match in snippet view article find links to article

descent theory" (PDF). arXiv:math/0412512. Bibcode:2004math.....12512V. Stacks Project, "The fpqc Topology." http://stacks.math.columbia.edu/tag/03NV

Double complex (568 words) [view diff] case mismatch in snippet view article find links to article

"Section 12.18 (0FNB): Double complexes and associated total complexes—The Stacks project". stacks.math.columbia.edu. Retrieved 2021-07-08. Weibel, Charles A

Functor represented by a scheme (1,261 words) [view diff] exact match in snippet view article find links to article

R\mapsto Y(R)} determines a morphism of schemes X →Y in a natural way. The Stacks Project, 01J5 The functor of points, Yoneda's lemmma, moduli spaces and universal

Ringed topos (836 words) [view diff] case mismatch in snippet view article find links to article

ISSN 0010-3616. "Section 26.15 (01JF): A representability criterion—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-04-28. The standard reference

Glossary of algebraic geometry (12,496 words) [view diff] exact match in snippet view article find links to article

arXiv:1410.1716 [math.AG]. Hartshorne 1977, Exercise II.3.11(d) The Stacks Project, Chapter 21, §4. Grothendieck & Dieudonné 1960, 4.2.1 Hartshorne 1977

Hilbert scheme (3,409 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-1-4008-7123-0 "Section 97.9 (0CZX): The Hilbert functor—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-06-17. "3264 and all that"

2-Yoneda lemma (1,245 words) [view diff] case mismatch in snippet view article find links to article

"94.5 The 2-Yoneda lemma—The Stacks project". stacks.math.columbia.edu. "Lemma 4.41.2 (2-Yoneda lemma)—The Stacks project". stacks.math.columbia.edu. "2

Derived category (4,514 words) [view diff] exact match in snippet view article find links to article

14. ISBN 978-3-642-85844-4. Weibel 1994, remark 10.4.5 and errata Stacks Project, tag 079P. Markarian, Nikita (2009). "The Atiyah class, Hochschild cohomology

Injective module (4,058 words) [view diff] case mismatch in snippet view article find links to article

submodule can be extended to the whole module. "Lemma 47.7.5 (08Z6)—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-02-25. Eisenbud. Introduction

Francis Mechner (2,745 words) [view diff] case mismatch in snippet view article find links to article

queenspaideiaschool.org/ Queens Paideia School Web site. Mechner, F. (1976). The STACKS project. Archives of The Mechner Foundation at 200 Central Park South, New York

Hochschild homology (3,399 words) [view diff] case mismatch in snippet view article find links to article

Geometry". arXiv:math/0506603. "Section 23.6 (09PF): Tate resolutions—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-12-31. Cartan, Henri; Eilenberg

Chow group (4,204 words) [view diff] exact match in snippet view article find links to article

geometry) Fulton. Intersection Theory, section 1.2 and Appendix A.3. Stacks Project, https://stacks.math.columbia.edu/tag/0BE9 Fulton, Intersection Theory

Reflection principle (3,612 words) [view diff] exact match in snippet view article find links to article

978-3-540-88866-6. "Section 3.8 (000F): Reflection principle". The Stacks Project. 2022. Retrieved 7 September 2022. T. Jech, 'Set Theory: The Third Millennium

Sheaf of modules (3,465 words) [view diff] case mismatch in snippet view article find links to article

"Section 30.2 (01X8): Čech cohomology of quasi-coherent sheaves—The Stacks project". stacks.math.columbia.edu. Retrieved 2023-12-07. Costa, Miró-Roig &

Moduli stack of elliptic curves (2,344 words) [view diff] case mismatch in snippet view article find links to article

American Mathematical Society, ISBN 978-1470427986 moduli+stack+of+elliptic+curves at the nLab "The moduli stack of elliptic curves", Stacks project

Integral element (5,312 words) [view diff] case mismatch in snippet view article find links to article

Exercise 35 "Section 32.14 (05JW): Universally closed morphisms—The Stacks project". stacks.math.columbia.edu. Retrieved 2020-05-11. Stein. Computational

Weyl algebra (4,173 words) [view diff] case mismatch in snippet view article find links to article

pp. 600–601. "Section 41.13 (039P): Étale and smooth morphisms—The Stacks project". stacks.math.columbia.edu. Retrieved 2024-09-29. "etale morphism of

Old Aberdeen Police Station (508 words) [view diff] case mismatch in snippet view article find links to article

was later converted into a flat roof, which the roof has tall chimney stacks project upwards. The brickwork is trimmed with granite string courses and moulded