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.
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We thank U. Stuhler for discussions and historical remarks.
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Schoemann, C., Wiedmann, S. Another proof of Grothendieck’s theorem on the splitting of vector bundles on the projective line. Arch. Math. 110, 573–580 (2018). https://doi.org/10.1007/s00013-018-1158-0
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DOI: https://doi.org/10.1007/s00013-018-1158-0