Vector bundles of rank 2 on the projective line over ℤ are considered. It is assumed that such a bundle E is trivial on a generic fiber, and its restriction to any special fiber is isomorphic either to O2 or to O(−1)⊕O(1). Under these assumptions it is proved that an exact sequence of the form 0→O(−2) → E →O(2) → 0 exists.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 452, 2016, pp. 202–217.
Translated by N. B. Lebedinskaya.
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Smirnov, A.L. Vector Bundles on P1ℤ with Simple Jumps. J Math Sci 232, 721–731 (2018). https://doi.org/10.1007/s10958-018-3901-2
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DOI: https://doi.org/10.1007/s10958-018-3901-2