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.