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

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 $\Lambda \cong k[T]^d$, discretely embedded into the vector space $V \cong K_\infty ^d$, where $K_\infty \cong k((1/T))$ is the completion of the field of rational functions k(T) at the place $\infty$ with the usual valuation.