Riemann-Roch's theorem in characteristic p

GPTKB entity

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