Wikipedia:WikiProject Mathematics/PlanetMath Exchange/14-XX Algebraic geometry
This page provides a list of all articles available at PlanetMath in the following topic:
- 14-XX Algebraic geometry.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
14-00 General reference works (handbooks, dictionaries, bibliographies, etc.) edit
- PM: affine space, id=1121 -- WP: affine space -- Status: A
- Jtwdog 21:35, 26 September 2005 (UTC)
- PM: affine variety, id=1123 -- WP: affine variety -- Status: A
- Jtwdog 21:35, 26 September 2005 (UTC)
- PM: dual isogeny, id=3226 -- WP: dual isogeny -- Status: M
- Jtwdog 21:35, 26 September 2005 (UTC)
- Juliusross 19:25, 14 May 2006 (UTC)
- PM: example of quasi-affine variety that is not affine, id=5729 -- WP: quasi-affine variety -- Status: N
- Jtwdog 15:31, 18 October 2005 (UTC)
- Probably not needed in WP Juliusross 18:18, 14 May 2006 (UTC)
- PM: finite morphism, id=3199 -- WP: finite morphism -- Status: M
- Juliusross 18:35, 14 May 2006 (UTC)
- PM: isogeny, id=3206 -- WP: elliptic curve -- Status: M
- Jtwdog 21:35, 26 September 2005 (UTC)
- PM: line bundle, id=4104 -- WP: line bundle -- Status: A
- Jtwdog 21:35, 26 September 2005 (UTC)
- PM: nonsingular variety, id=1117 -- WP: nonsingular variety -- Status: A
- Jtwdog 15:34, 18 October 2005 (UTC)
- PM: Picard group, id=3216 -- WP: Picard group -- Status: A
- Jtwdog 21:35, 26 September 2005 (UTC)
- PM: projective space, id=1122 -- WP: projective space -- Status: A
- Jtwdog 15:31, 18 October 2005 (UTC)
- PM: projective variety, id=1124 -- WP: projective variety -- Status: A
- Jtwdog 15:31, 18 October 2005 (UTC)
- PM: quasi-finite morphism, id=3207 -- WP: quasi-finite morphism -- Status: A
- Jtwdog 15:31, 18 October 2005 (UTC)
- PM: variety, id=5730 -- WP: algebraic variety -- Status: A
- Jtwdog 15:31, 18 October 2005 (UTC)
- PM: affine space, id=7013 -- WP guess: affine space -- Status:
- PM: algebraic geometry, id=5722 -- WP guess: algebraic geometry -- Status: NM
- PM: algebraic manifold, id=7518 -- WP guess: algebraic manifold -- Status: A
- PM: analytic algebraic function, id=7517 -- WP guess: analytic algebraic function -- Status: NM
- PM: bibliography for algebraic geometry, id=5682 -- WP guess: bibliography for algebraic geometry -- Status: ?
14A05 Relevant commutative algebra edit
14A10 Varieties and morphisms edit
- PM: algebraic map, id=4641 -- WP: algebraic variety -- Status: NM
- Jtwdog 15:48, 18 October 2005 (UTC)
- PM: algebraic sets and polynomial ideals, id=3513 -- WP: Nullstellensatz -- Status: A
- Jtwdog 15:48, 18 October 2005 (UTC)
- PM: alternate characterizations of the noetherian condition, id=5724 -- WP: noetherian topological space -- Status: A
Juliusross 15:54, 14 May 2006 (UTC)
- PM: Bézout's theorem (Algebraic Geometry), id=6188 -- WP: Bézout's theorem -- Status: A
- Jtwdog 15:48, 18 October 2005 (UTC)
- PM: irreducible, id=1109 -- WP: irreducible component -- Status: M
- Juliusross 18:47, 14 May 2006 (UTC)
- PM: irreducible component, id=3107 -- WP: irreducible component -- Status: M
- Juliusross 15:49, 14 May 2006 (UTC)
- PM: noetherian topological space, id=3465 -- WP: noetherian topological space -- Status: M
Juliusross 15:49, 14 May 2006 (UTC)
- PM: regular map, id=1125 -- WP: algebraic variety -- Status: NM
- Jtwdog 15:48, 18 October 2005 (UTC)
- PM: structure sheaf, id=2903 -- WP: structure sheaf -- Status: A
- Jtwdog 16:23, 6 October 2005 (UTC)
- PM: Zariski topology, id=2899 -- WP: Zariski topology -- Status: NM
- This wikipedia article is not in the best of shape. It really needs clean-up more than merging. Jtwdog 16:23, 6 October 2005 (UTC)
- PM: ind-variety, id=7383 -- WP guess: ind-variety -- Status:
- PM: isomorphism of varieties, id=6838 -- WP guess: algebraic variety -- Status: M
- Juliusross 23:06, 14 May 2006 (UTC)
- PM: proof of alternate characterizations of the noetherian condition, id=7274 -- WP guess: proof of alternate characterizations of the noetherian condition -- Status: N
- PM: countable algebraic sets, id=7696new! -- WP guess: countable algebraic sets -- Status:
- PM: lemma on projection of countable sets, id=7700new! -- WP guess: lemma on projection of countable sets -- Status:
14A15 Schemes and morphisms edit
- PM: closed immersion, id=3165 -- WP guess: closed immersion -- Status: A
- Jtwdog 15:57, 18 October 2005 (UTC)
- Juliusross 23:09, 14 May 2006 (UTC)
- PM: coherent sheaf, id=4596 -- WP: coherent sheaf -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: example of fibre product, id=5558 -- WP guess: example of fibre product -- Status: N
- Jtwdog 15:57, 18 October 2005 (UTC)
- PM: example of functor of points of a scheme, id=5612 -- WP: functor of points -- Status: NM
- Jtwdog 15:57, 18 October 2005 (UTC)
- Just my opinion this should be Status: N Juliusross 23:14, 14 May 2006 (UTC)
- PM: fibre product, id=3142 -- WP: fibre product -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: flat morphism, id=5614 -- WP: flat morphism -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: general linear group scheme, id=5617 -- WP: general linear group -- Status: NM
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: group scheme, id=5616 -- WP: group scheme -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: group scheme of multiplicative units, id=5567 -- WP: group scheme of multiplicative units -- Status: NM
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: locally ringed space, id=2890 -- WP: locally ringed space -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: morphism of schemes induces a map of points, id=5610 -- WP guess: morphism of schemes induces a map of points -- Status: N
- Jtwdog 15:57, 18 October 2005 (UTC)
- PM: prime spectrum, id=2898 -- WP: prime spectrum -- Status: A
- Jtwdog 18:46, 17 October 2005 (UTC)
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: separated scheme, id=3166 -- WP: separated scheme -- Status: A
- Jtwdog 15:57, 18 October 2005 (UTC)
- PM: singular set, id=3852 -- WP: singular set -- Status: A
- Juliusross 23:17, 14 May 2006 (UTC)
- PM: Étalé morphism, id=5559 -- WP guess: étale morphism -- Status: NC
- Jtwdog 18:46, 17 October 2005 (UTC)
- PM: V(I)=\emptyset implies I=R, id=8199new! -- WP guess: V(I)=\emptyset implies I=R -- Status:
- PM: proof that \operatorname{Spec}(R) is quasi-compact, id=8198new! -- WP guess: proof that \operatornameSpec(R) is quasi-compact -- Status:
14A20 Generalizations (algebraic spaces, stacks) edit
- Jtwdog 15:58, 18 October 2005 (UTC)
14A25 Elementary questions edit
- Jtwdog 16:01, 18 October 2005 (UTC)
14A99 Miscellaneous edit
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: Cartier divisor, id=4617 -- WP: Cartier divisor -- Status: A
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: general position, id=4262 -- WP: general position -- Status: A
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: height of a prime ideal, id=3146 -- WP: height of a prime ideal -- Status: NM
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: invertible sheaf, id=4619 -- WP: invertible sheaf -- Status: A
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: locally free, id=4618 -- WP: locally free sheaf -- Status: M
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: normal irreducible varieties are nonsingular in codimension 1, id=3853 -- WP: normal variety -- Status: NM
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: Serre's twisting theorem, id=4623 -- WP: ample -- Status: NM
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: sheaf of meromorphic functions, id=4614 -- WP guess: locally ringed space -- Status: NM
- Jtwdog 16:16, 18 October 2005 (UTC)
- PM: very ample, id=4621 -- WP: very ample -- Status: A
- Jtwdog 16:16, 18 October 2005 (UTC)
14Axx Foundations edit
14C17 Intersection theory, characteristic classes, intersection multiplicities edit
- PM: mod 2 intersection number, id=4990 -- WP guess: mod 2 intersection number -- Status: N
- The article doesn't seem to exist on PM. Jtwdog 18:30, 19 October 2005 (UTC)
14C20 Divisors, linear systems, invertible sheaves edit
- PM: divisor, id=1102 -- WP: divisor (algebraic geometry) -- Status: A
- Jtwdog 16:00, 18 October 2005 (UTC)
- PM: algebraic equivalence of divisors, id=7474 -- WP guess: Linear_equivalence -- Status: A
- PM: Néron-Severi group, id=7475 -- WP guess: Néron-Severi group -- Status:
- PM: Weil divisors on schemes, id=7473 -- WP guess: Divisor (mathematics) -- Status: A
- PM: intersection divisor for a quartic, id=7702new! -- WP guess: intersection divisor for a quartic -- Status:
14Cxx Cycles and subschemes edit
14E05 Rational and birational maps edit
- PM: general type, id=1104 -- WP guess: general type -- Status: A
- Jtwdog 16:03, 18 October 2005 (UTC)
- PM: Kodaira-Itaka dimension, id=8308new! -- WP guess: Kodaira-Itaka dimension -- Status:
14E22 Ramification problems edit
14Exx Birational geometry edit
- PM: direct image (functor), id=1101 -- WP: direct image functor -- Status: C
- Jtwdog 21:28, 28 October 2005 (UTC)
- PM: sheaf, id=2878 -- WP: sheaf (mathematics) -- Status: A
- Jtwdog 19:50, 28 September 2005 (UTC)
- PM: sheafification, id=2889 -- WP: sheafification -- Status: A
- Jtwdog 19:50, 28 September 2005 (UTC)
- PM: stalk, id=2881 -- WP: stalk of a sheaf -- Status: A
- Jtwdog 19:50, 28 September 2005 (UTC)
- PM: Étalé space, id=7608 -- WP guess: Étalé space -- Status:
- PM: presheaf of a topological basis, id=8519new! -- WP guess: presheaf of a topological basis -- Status:
14F20 Étalé and other Grothendieck topologies and cohomologies edit
- PM: sheaf, id=5648 -- WP guess: sheaf (mathematics) -- Status: A
- Jtwdog 18:39, 19 October 2005 (UTC)
- PM: sheafification, id=5654 -- WP guess: sheafification -- Status: A
- Jtwdog 18:39, 19 October 2005 (UTC)
- PM: site, id=1730 -- WP guess: Grothendieck topology -- Status: A
- Jtwdog 18:39, 19 October 2005 (UTC)
- PM: small site on a scheme, id=5560 -- WP guess: Grothendieck topology -- Status: NM
- Jtwdog 18:39, 19 October 2005 (UTC)
- PM: Étalé cohomology, id=5666 -- WP guess: Étalé cohomology -- Status: A
- Jtwdog 18:39, 19 October 2005 (UTC)
14F25 Classical real and complex cohomology edit
- PM: Serre duality, id=4595 -- WP: Serre duality -- Status: A
- Jtwdog 19:51, 28 September 2005 (UTC)
- PM: sheaf cohomology, id=4587 -- WP: sheaf cohomology -- Status: A
- Jtwdog 19:51, 28 September 2005 (UTC)
14F35 Homotopy theory; fundamental groups edit
- Jtwdog 18:43, 19 October 2005 (UTC)
- PM: Étalé fundamental group, id=5627 -- WP: Étalé fundamental group -- Status: C
- Jtwdog 22:02, 28 October 2005 (UTC)
14F40 de Rham cohomology edit
14F42 Motivic cohomology edit
- PM: motivic cohomology, id=8969new! -- WP guess: motivic cohomology -- Status:
14F99 Miscellaneous edit
- PM: Leray spectral sequence for an affine morphism, id=5561 -- WP: Leray spectral sequence -- Status: NM
- Jtwdog 21:45, 28 October 2005 (UTC)
14Fxx (Co)homology theory edit
14G05 Rational points edit
- PM: Hasse principle, id=4581 -- WP: Hasse principle -- Status: A
- Jtwdog 19:51, 28 September 2005 (UTC)
- PM: Hasse-Minkowski theorem, id=7143 -- WP guess: Hasse-Minkowski theorem -- Status:
- PM: Faltings's theorem, id=7968new! -- WP guess: Faltings's theorem -- Status:
- PM: Weil conjectures, id=7670new! -- WP guess: Weil conjectures -- Status:
14G15 Finite ground fields edit
14G20 Local ground fields edit
- PM: global field, id=9114new! -- WP guess: global field -- Status:
14G25 Global ground fields edit
14Gxx Arithmetic problems. Diophantine geometry edit
14H37 Automorphisms edit
- PM: Frobenius morphism, id=4602 -- WP: Frobenius morphism -- Status: A
- Jtwdog 18:52, 17 October 2005 (UTC)
14H45 Special curves and curves of low genus edit
- PM: archimedean spiral, id=5486 -- WP: archimedean spiral -- Status: A
- Jtwdog 18:43, 19 October 2005 (UTC)
- PM: Fermat's spiral, id=5487 -- WP: Fermat's spiral -- Status: A
- Jtwdog 18:43, 19 October 2005 (UTC)
- Jtwdog 18:43, 19 October 2005 (UTC)
14H50 Plane and space curves edit
- PM: torsion (space curve), id=1634 -- WP guess: torsion (space curve) -- Status:
14H52 Elliptic curves edit
- PM: bad reduction, id=4553 -- WP guess: bad reduction -- Status:
- PM: Birch and Swinnerton-Dyer conjecture, id=4561 -- WP guess: Birch and Swinnerton-Dyer conjecture -- Status:
- PM: bound for the rank of an elliptic curve, id=5908 -- WP guess: bound for the rank of an elliptic curve -- Status:
- PM: conductor of an elliptic curve, id=4563 -- WP guess: conductor of an elliptic curve -- Status:
- PM: examples of torsion subgroups of elliptic curves, id=5871 -- WP guess: examples of torsion subgroups of elliptic curves -- Status:
- PM: Hasse's bound for elliptic curves over finite fields, id=4686 -- WP guess: Hasse's bound for elliptic curves over finite fields -- Status:
- PM: height function, id=4549 -- WP guess: height function -- Status:
- PM: j-invariant, id=4565 -- WP: j-invariant -- Status: A
- Jeekc 16:37, 22 December 2005 (UTC)
- PM: L-series of an elliptic curve, id=4560 -- WP guess: L-series of an elliptic curve -- Status:
- PM: Mazur's theorem on torsion of elliptic curves, id=4607 -- WP guess: Mazur's theorem on torsion of elliptic curves -- Status:
- PM: Mordell curve, id=4566 -- WP guess: Mordell curve -- Status:
- PM: Mordell-Weil theorem, id=1725 -- WP guess: Mordell-Weil theorem -- Status:
- PM: Nagell-Lutz theorem, id=4608 -- WP guess: Nagell-Lutz theorem -- Status:
- PM: rank of an elliptic curve, id=4550 -- WP guess: rank of an elliptic curve -- Status:
- PM: Selmer group, id=4586 -- WP guess: Selmer group -- Status:
- PM: supersingular, id=1891 -- WP guess: supersingular -- Status:
- PM: the torsion subgroup of an elliptic curve injects in the reduction of the curve, id=4688 -- WP guess: the torsion subgroup of an elliptic curve injects in the reduction of the curve -- Status:
- PM: criterion of Néron-Ogg-Shafarevich, id=9582new! -- WP guess: criterion of Néron-Ogg-Shafarevich -- Status:
14H99 Miscellaneous edit
- PM: genus, id=1116 -- WP: Genus (mathematics) -- Status: A
- Jtwdog 18:31, 17 October 2005 (UTC)
- PM: projective curve, id=2985 -- WP: projective curve -- Status: A
- Jtwdog 18:31, 17 October 2005 (UTC)
- PM: proof of Riemann-Roch theorem, id=4599 -- WP (none) -- Status: N
- Jtwdog 18:31, 17 October 2005 (UTC)
- PM: Riemann-Roch theorem for curves, id=1098 -- WP: Riemann-Roch theorem -- Status: A
- Jtwdog 18:50, 19 October 2005 (UTC)
- PM: space of functions associated to a divisor, id=5640 -- WP: Riemann-Roch theorem -- Status: A
- Jtwdog 18:50, 19 October 2005 (UTC)
- PM: Hurwitz genus formula, id=7966new! -- WP guess: Hurwitz genus formula -- Status:
14Hxx Curves edit
14J25 Special surfaces edit
- PM: cylindroid, id=6221 -- WP guess: cylindroid -- Status:
- PM: ruled surface, id=6222 -- WP: ruled surface -- Status: A
- Jtwdog 18:26, 17 October 2005 (UTC)
- PM: cylindroid, id=8897new! -- WP guess: cylindroid -- Status:
- PM: Plücker's conoid, id=8956new! -- WP guess: Plücker's conoid -- Status:
14J27 Elliptic surfaces edit
- PM: elliptic surface, id=7476 -- WP guess: elliptic surface -- Status:
- PM: Shioda-Tate formula, id=7479 -- WP guess: Shioda-Tate formula -- Status:
14J70 Hypersurfaces edit
- PM: hypersurface, id=6099 -- WP: hypersurface -- Status: A
- Jtwdog 18:24, 17 October 2005 (UTC)
14J80 Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) edit
- PM: Donaldson Freedman exotic R4, id=7552 -- WP guess: Donaldson Freedman exotic R4 -- Status:
- PM: Donaldson's theorem, id=7550 -- WP guess: Donaldson's theorem -- Status:
- PM: exotic R4's, id=7551 -- WP: exotic R4's -- Status: NM
- Paul August ☎ 20:42, 8 May 2006 (UTC)
14Jxx Surfaces and higher-dimensional varieties edit
14K25 Theta functions edit
14K99 Miscellaneous edit
- PM: abelian variety, id=5742 -- WP: abelian variety -- Status: A
- Jtwdog 19:58, 28 September 2005 (UTC)
- PM: group variety, id=5582 -- WP: group variety -- Status: A
- Jtwdog 19:58, 28 September 2005 (UTC)
14Kxx Abelian varieties and schemes edit
14L10 Group varieties edit
14L15 Group schemes edit
14L17 Affine algebraic groups, hyperalgebra constructions edit
- PM: affine algebraic group, id=4638 -- WP: affine algebraic group -- Status: A
- Jtwdog 19:55, 28 September 2005 (UTC)
- PM: algebraic torus, id=4636 -- WP: algebraic torus -- Status: A
- Jtwdog 19:55, 28 September 2005 (UTC)
14L24 Geometric invariant theory edit
- PM: Quiver, id=7478 -- WP (none) -- Status:
- Don't know if this should be copied or not. Paul August ☎ 20:23, 8 May 2006 (UTC)
14Lxx Algebraic groups edit
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) edit
- PM: normal variety, id=3856 -- WP: normal variety -- Status: A
- Jtwdog 18:24, 17 October 2005 (UTC)
14M12 Determinantal varieties edit
14M15 Grassmannians, Schubert varieties, flag manifolds edit
- PM: Borel-Bott-Weil theorem, id=4585 -- WP: Borel-Bott-Weil theorem -- Status: A
- Jtwdog 19:52, 28 September 2005 (UTC)
- PM: flag variety, id=4034 -- WP: flag variety -- Status: A
- Jtwdog 19:52, 28 September 2005 (UTC)
14Mxx Special varieties edit
14N05 Projective techniques edit
- PM: Hodge Theory, id=7184 -- WP: Hodge theory -- Status:
- Don't know whether there is anything to be merged here or not.
14Nxx Projective and enumerative geometry edit
- PM: semialgebraic set, id=8997new! -- WP guess: semialgebraic set -- Status:
- PM: Tarski-Seidenberg theorem, id=8998new! -- WP guess: Tarski-Seidenberg theorem -- Status:
14P15 Real analytic and semianalytic sets edit
- PM: subanalytic set, id=8999new! -- WP guess: subanalytic set -- Status: C
14P20 Nash functions and manifolds edit
14Pxx Real algebraic and real analytic geometry edit
14Q99 Miscellaneous edit
14Qxx Computational aspects in algebraic geometry edit
14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) edit
14R15 Jacobian problem edit
- PM: Jacobian conjecture, id=3935 -- WP: Jacobian conjecture -- Status: A
- Jtwdog 19:56, 28 September 2005 (UTC)