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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2022 Volume 511, Pages 137–160 (Mi znsl7211)

This article is cited in 1 paper

Finiteness of the number of classes of vector bundles on $\mathbb{P}^1_{\mathbb{Z}}$ with jumps of height $2$

V. M. Polyakov

Saint Petersburg State University

Abstract: We consider vector bundles of rank $2$ with jumps of heights $1$ and $2$ and a trivial generic fiber on the arithmetic surface $\mathbb{P}^1_{\mathbb{Z}}$. The finiteness of the number of isomorphism classes of such vector bundles with a fixed discriminant and, as a consequence, with a fixed genus is obtained.

Key words and phrases: vector bundle, arithmetic surface, projective line, jumps, genus.

UDC: 512.75

Received: 06.10.2022


 English version:
Journal of Mathematical Sciences (New York), 2024, 286:6, 912–927


© Steklov Math. Inst. of RAS, 2025