Vector bundles on $\mathbf P^1_\mathbb Z$ with simple jumps
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 202-217
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We consider vector bundles with rank 2 over the projective line over $\mathbb Z$. Assume that such a bundle $E$ is trivial on the generic fiber, and its restriction to any special fiber is isomorphic either to $\mathcal O^2$ or to $\mathcal O(-1)\oplus\mathcal O(1)$. Under these assumptions we prove that there exists an exact sequence of the form $0\to\mathcal O(-2)\to E\to\mathcal O(2)\to0$.
@article{ZNSL_2016_452_a10,
author = {A. L. Smirnov},
title = {Vector bundles on $\mathbf P^1_\mathbb Z$ with simple jumps},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {202--217},
year = {2016},
volume = {452},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a10/}
}
A. L. Smirnov. Vector bundles on $\mathbf P^1_\mathbb Z$ with simple jumps. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 202-217. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a10/
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