Grothendieck's theorem on vector bundles on the projective line

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:alsoKnownAs	gptkb:Grothendieck's_splitting_theorem
gptkbp:appliesTo	projective line over a field
gptkbp:author	gptkb:Alexander_Grothendieck
gptkbp:consequence	Every vector bundle on the projective line is isomorphic to a direct sum of line bundles of the form O(n).
gptkbp:context	gptkb:vector_bundles projective line
gptkbp:field	gptkb:algebraic_geometry
https://www.w3.org/2000/01/rdf-schema#label	Grothendieck's theorem on vector bundles on the projective line
gptkbp:implies	classification of vector bundles on the projective line
gptkbp:influenced	study of vector bundles on higher-dimensional varieties
gptkbp:main_statement	Every vector bundle on the projective line over a field splits as a direct sum of line bundles.
gptkbp:publishedIn	gptkb:Séminaire_Bourbaki,_1957
gptkbp:relatedConcept	gptkb:Birkhoff–Grothendieck_theorem direct sum decomposition line bundle
gptkbp:year	1957
gptkbp:bfsParent	gptkb:Serre's_theorem_on_the_splitting_of_vector_bundles
gptkbp:bfsLayer	6