Geodesic
Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 218-237 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study vector bundles on the projective line over a Dedekind domain $A$. In the case where $A$ is a PID, we get a complete classification of rank 2 vector bundles with generic fiber $\mathcal{O\oplus O}(1)$ and with special fibers isomorphic either to $\mathcal{O\oplus O}(1)$ or $\mathcal O(-1)\oplus\mathcal O(2)$. 
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     author = {S. S. Iakovenko},
     title = {Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--237},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a11/}
}
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S. S. Iakovenko. Vector bundles on $\mathbf P^1_\mathbb Z$ with generic fiber $\mathcal{O\oplus O}(1)$ and simple jumps. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 30, Tome 452 (2016), pp. 218-237. http://geodesic.mathdoc.fr/item/ZNSL_2016_452_a11/

[1] K. Okonek, M. Shnaider, Kh. Shpindler, Vektornye rassloeniya na kompleksnykh proektivnykh prostranstvakh, Mir, Moskva, 1984 | MR

[2] A. Smirnov, “On filtrations of vector bundles over $\mathbf P^1_\mathbb Z$”, Arithmetic and Geometry, London Math. Soc. Lect. Note Series, 420, Cambridge Univ. Press, 2015, 436–457 | MR

[3] Zh.-P. Serr, Kogerentnye algebraicheskie puchki. Rassloennye prostranstva i ikh prilozheniya, izd-vo Inostrannoi literatury, Moskva, 1958

[4] Ch. C. Hanna, “Subbundles of vector bundles on the projective line”, J. Algebra, 52:2 (1978), 322–327 | DOI | MR | Zbl

[5] B. L. Van der Varden, Algebra, Mir, Moskva, 1976

[6] A. L. Smirnov, S. S. Yakovenko, Postroenie lineinoi filtratsii dlya rassloenii ranga 2 na $\mathbf Pro_\mathbb Z^1$, Preprint, POMI, 2015

[7] R. Khartskhorn, Algebraicheskaya geometriya, Mir, Moskva, 1981

[8] D. Quillen, “Projective modules over polynomial rings”, Invent. Math., 36 (1976), 167–171 | DOI | MR | Zbl

[9] A. A. Suslin, “Proektivnye moduli nad koltsami mnogochlenov svobodny”, Dokl. AN SSSR, 229:5 (1976), 1063–1066 | Zbl