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- Grothendieck–Riemann–Roch_theorem abstract "In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a generalisation of the classical Riemann–Roch theorem for line bundles on compact Riemann surfaces.Riemann–Roch type theorems relate Euler characteristics of the cohomology of a vector bundle with their topological degrees, or more generally their characteristic classes in (co)homology or algebraic analogues thereof. The classical Riemann–Roch theorem does this for curves and line bundles, whereas the Hirzebruch–Riemann–Roch theorem generalises this to vector bundles over manifolds. The Grothendieck–Riemann–Roch theorem sets both theorems in a relative situation of a morphism between two manifolds (or more general schemes) and changes the theorem from a statement about a single bundle, to one applying to chain complexes of sheaves.The theorem has been very influential, not least for the development of the Atiyah–Singer index theorem. Conversely, complex analytic analogues of the Grothendieck–Riemann–Roch theorem can be proved using the index theorem for families. Alexander Grothendieck gave a first proof in a 1957 manuscript, later published. Armand Borel and Jean-Pierre Serre wrote up and published Grothendieck's proof in 1958. Later, Grothendieck and his collaborators simplified and generalized the proof.".
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Category:Topological_methods_of_algebraic_geometry.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Chern_class.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Field_(mathematics).
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Grothendieck_group.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Hirzebruch–Riemann–Roch_theorem.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Jean-Pierre_Serre.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Mathematics.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Mathematische_Arbeitstagung.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Morphism.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Proper_morphism.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Quasi-projective_variety.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Rational_number.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Sheaf_(mathematics).
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Smooth_morphism.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Todd_class.
- Grothendieck–Riemann–Roch_theorem wikiPageWikiLink Topological_degree_theory.
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- Grothendieck–Riemann–Roch_theorem wikiPageWikiLinkText "Grothendieck–Riemann–Roch theorem".
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- Grothendieck–Riemann–Roch_theorem subject Category:Theorems_in_algebraic_geometry.
- Grothendieck–Riemann–Roch_theorem subject Category:Topological_methods_of_algebraic_geometry.
- Grothendieck–Riemann–Roch_theorem hypernym Result.
- Grothendieck–Riemann–Roch_theorem type Method.
- Grothendieck–Riemann–Roch_theorem type Redirect.
- Grothendieck–Riemann–Roch_theorem type Theorem.
- Grothendieck–Riemann–Roch_theorem comment "In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology.".
- Grothendieck–Riemann–Roch_theorem label "Grothendieck–Riemann–Roch theorem".
- Grothendieck–Riemann–Roch_theorem sameAs Q1899432.
- Grothendieck–Riemann–Roch_theorem sameAs Théorème_de_Grothendieck-Hirzebruch-Riemann-Roch.
- Grothendieck–Riemann–Roch_theorem sameAs 그로텐디크-리만-로흐_정리.
- Grothendieck–Riemann–Roch_theorem sameAs Stelling_van_Grothendieck-Hirzebruch-Riemann-Roch.
- Grothendieck–Riemann–Roch_theorem sameAs m.058m3p.
- Grothendieck–Riemann–Roch_theorem sameAs Q1899432.
- Grothendieck–Riemann–Roch_theorem wasDerivedFrom Grothendieck–Riemann–Roch_theorem?oldid=663265293.
- Grothendieck–Riemann–Roch_theorem depiction Grothendieck-Riemann-Roch.jpg.
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