Wikipedia:WikiProject Mathematics/PlanetMath Exchange/14-XX Algebraic geometry
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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
- PM: affine variety, id=1123 -- WP: affine variety -- Status: A
- PM: dual isogeny, id=3226 -- WP: dual isogeny -- Status: M
- 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
- PM: isogeny, id=3206 -- WP: elliptic curve -- Status: M
- PM: line bundle, id=4104 -- WP: line bundle -- Status: A
- PM: nonsingular variety, id=1117 -- WP: nonsingular variety -- Status: A
- PM: Picard group, id=3216 -- WP: Picard group -- Status: A
- PM: projective space, id=1122 -- WP: projective space -- Status: A
- PM: projective variety, id=1124 -- WP: projective variety -- Status: A
- PM: quasi-finite morphism, id=3207 -- WP: quasi-finite morphism -- Status: A
- PM: variety, id=5730 -- WP: algebraic variety -- Status: A
- 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
- PM: algebraic sets and polynomial ideals, id=3513 -- WP: Nullstellensatz -- Status: A
- 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
- PM: irreducible, id=1109 -- WP: irreducible component -- Status: M
- PM: irreducible component, id=3107 -- WP: irreducible component -- Status: M
- 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
- PM: structure sheaf, id=2903 -- WP: structure sheaf -- Status: A
- 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
- 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
- PM: coherent sheaf, id=4596 -- WP: coherent sheaf -- Status: A
- PM: example of fibre product, id=5558 -- WP guess: example of fibre product -- Status: N
- 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
- PM: flat morphism, id=5614 -- WP: flat morphism -- Status: A
- PM: general linear group scheme, id=5617 -- WP: general linear group -- Status: NM
- PM: group scheme, id=5616 -- WP: group scheme -- Status: A
- PM: group scheme of multiplicative units, id=5567 -- WP: group scheme of multiplicative units -- Status: NM
- PM: locally ringed space, id=2890 -- WP: locally ringed space -- Status: A
- PM: morphism of schemes induces a map of points, id=5610 -- WP guess: morphism of schemes induces a map of points -- Status: N
- PM: prime spectrum, id=2898 -- WP: prime spectrum -- Status: A
- PM: separated scheme, id=3166 -- WP: separated scheme -- Status: A
- PM: singular set, id=3852 -- WP: singular set -- Status: A
- PM: Étalé morphism, id=5559 -- WP guess: étale morphism -- Status: NC
- 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]14A25 Elementary questions
[edit]14A99 Miscellaneous
[edit]- PM: Cartier divisor, id=4617 -- WP: Cartier divisor -- Status: A
- PM: general position, id=4262 -- WP: general position -- Status: A
- PM: height of a prime ideal, id=3146 -- WP: height of a prime ideal -- Status: NM
- PM: invertible sheaf, id=4619 -- WP: invertible sheaf -- Status: A
- PM: locally free, id=4618 -- WP: locally free sheaf -- Status: M
- PM: normal irreducible varieties are nonsingular in codimension 1, id=3853 -- WP: normal variety -- Status: NM
- PM: Serre's twisting theorem, id=4623 -- WP: ample -- Status: NM
- PM: sheaf of meromorphic functions, id=4614 -- WP guess: locally ringed space -- Status: NM
- PM: very ample, id=4621 -- WP: very ample -- Status: A
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
- 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
- PM: Kodaira-Itaka dimension, id=8308new! -- WP guess: Kodaira-Itaka dimension -- Status:
14E22 Ramification problems
[edit]14Exx Birational geometry
[edit]14F05 Vector bundles, sheaves, related constructions
[edit]- PM: direct image (functor), id=1101 -- WP: direct image functor -- Status: C
- PM: sheaf, id=2878 -- WP: sheaf (mathematics) -- Status: A
- PM: sheafification, id=2889 -- WP: sheafification -- Status: A
- PM: stalk, id=2881 -- WP: stalk of a sheaf -- Status: A
- 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
- PM: sheafification, id=5654 -- WP guess: sheafification -- Status: A
- PM: site, id=1730 -- WP guess: Grothendieck topology -- Status: A
- PM: small site on a scheme, id=5560 -- WP guess: Grothendieck topology -- Status: NM
- PM: Étalé cohomology, id=5666 -- WP guess: Étalé cohomology -- Status: A
14F25 Classical real and complex cohomology
[edit]- PM: Serre duality, id=4595 -- WP: Serre duality -- Status: A
- PM: sheaf cohomology, id=4587 -- WP: sheaf cohomology -- Status: A
14F35 Homotopy theory; fundamental groups
[edit]- PM: Étalé fundamental group, id=5627 -- WP: Étalé fundamental group -- Status: C
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
14Fxx (Co)homology theory
[edit]14G05 Rational points
[edit]- PM: Hasse principle, id=4581 -- WP: Hasse principle -- Status: A
- 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:
14G10 Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
[edit]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
14H45 Special curves and curves of low genus
[edit]- PM: archimedean spiral, id=5486 -- WP: archimedean spiral -- Status: A
- PM: Fermat's spiral, id=5487 -- WP: Fermat's spiral -- Status: A
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
- 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
- PM: projective curve, id=2985 -- WP: projective curve -- Status: A
- PM: proof of Riemann-Roch theorem, id=4599 -- WP (none) -- Status: N
- PM: Riemann-Roch theorem for curves, id=1098 -- WP: Riemann-Roch theorem -- Status: A
- PM: space of functions associated to a divisor, id=5640 -- WP: Riemann-Roch theorem -- Status: A
- 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
- 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
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
14Jxx Surfaces and higher-dimensional varieties
[edit]14K25 Theta functions
[edit]14K99 Miscellaneous
[edit]- PM: abelian variety, id=5742 -- WP: abelian variety -- Status: A
- PM: group variety, id=5582 -- WP: group variety -- Status: A
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
- PM: algebraic torus, id=4636 -- WP: algebraic torus -- Status: A
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
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
- PM: flag variety, id=4034 -- WP: flag variety -- Status: A
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]14P10 Semialgebraic sets and related spaces
[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