Another proof of Grothendieck's theorem on the splitting of vector bundles on the projective line

2017/12/08 by Schoemann, Claudia, Wiedmann, Stefan
#14H60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.03056

Abstract

This note contains another proof of Grothendieck`s theorem on the splitting of vector bundles on the projective line over a field k. Actually the proof is formulated entirely in the classical terms of a lattice Λ≅ k[T]^d, discretely embedded into the vector space V ≅ K_∞^d, where K_∞ ≅ k((1/T)) is the completion of the field of rational functions k(T) at the place ∞ with the usual valuation.

Related

• Extension de fibres vectoriels et profondeur
• Vector Bundles over Projectivoid Line
• The Birkhoff-Grothendieck theorem
• Grothendieck-Lefschetz for vector bundles
• Splitting of Vector Bundles on Toric Varieties