Riemann-Roch's theorem in characteristic p
GPTKB entity
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Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Algebraic_curves
Fields of positive characteristic |
| gptkbp:citation |
Hartshorne, R. Algebraic Geometry (1977)
Zariski, O. (1932). The theorem of Riemann-Roch for high powers of an invertible divisor on an algebraic surface. |
| gptkbp:concerns |
gptkb:Sheaf_cohomology
Divisors |
| gptkbp:field |
gptkb:Algebraic_geometry
|
| gptkbp:generalizes |
gptkb:Riemann-Roch_theorem
|
| https://www.w3.org/2000/01/rdf-schema#label |
Riemann-Roch's theorem in characteristic p
|
| gptkbp:notable_for |
Frobenius morphism effects
Pathologies in cohomology |
| gptkbp:provenBy |
gptkb:Oscar_Zariski
|
| gptkbp:relatedTo |
gptkb:Serre_duality
gptkb:Weil_conjectures Zariski's work |
| gptkbp:state |
The dimension of the space of sections of a line bundle on a curve is related to the degree and genus, with possible modifications in characteristic p
|
| gptkbp:usedIn |
Study of algebraic curves over finite fields
|
| gptkbp:yearProved |
1930s
|
| gptkbp:bfsParent |
gptkb:Ernst_Witt
|
| gptkbp:bfsLayer |
4
|