Geodesic
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

Voir la notice de l'article provenant de la source Math-Net.Ru

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},
     publisher = {mathdoc},
     volume = {452},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a10/}
}
TY  - JOUR
AU  - A. L. Smirnov
TI  - Vector bundles on $\mathbf P^1_\mathbb Z$ with simple jumps
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 202
EP  - 217
VL  - 452
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a10/
LA  - ru
ID  - ZNSL_2016_452_a10
ER  - 
%0 Journal Article
%A A. L. Smirnov
%T Vector bundles on $\mathbf P^1_\mathbb Z$ with simple jumps
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 202-217
%V 452
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a10/
%G ru
%F 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/