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Sbornik: Mathematics, 2017, Volume 208, Issue 4, Pages 568–584
DOI: https://doi.org/10.1070/SM8775
(Mi sm8775)
 

This article is cited in 4 scientific papers (total in 4 papers)

Construction of a linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$

A. L. Smirnova, S. S. Yakovenkob

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
References:
Abstract: We obtain an algorithm for the construction of a filtration with linear factors for vector bundles of rank 2 over the surface $\mathbf{P}^1_A$, where $A$ is a Euclidean domain. In other words, we produce an algorithm that, for an invertible $2$-matrix $\sigma$ over the ring $A[x,x^{-1}]$, constructs matrices $\lambda$ over $A[x]$ and $\rho$ over $A[x^{-1}]$ for which $\lambda\sigma\rho$ is an upper triangular matrix.
Bibliography: 13 titles.
Keywords: vector bundle, arithmetic surface, projective line, filtration, reduction.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00750-а
Russian Science Foundation 14-21-00035
A. L. Smirnov's research was supported by the Russian Foundation for Basic Research (grant no. 16-01-00750_a). The first version of the main algorithm was obtained by S. S. Yakovenko with the support of the Russian Science Foundation (grant no. 14-21-00035).
Received: 04.07.2016 and 02.11.2016
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 4, Pages 111–128
DOI: https://doi.org/10.4213/sm8775
Bibliographic databases:
Document Type: Article
UDC: 512.723
MSC: Primary 14H60; Secondary 13F07
Language: English
Original paper language: Russian
Citation: A. L. Smirnov, S. S. Yakovenko, “Construction of a linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$”, Mat. Sb., 208:4 (2017), 111–128; Sb. Math., 208:4 (2017), 568–584
Citation in format AMSBIB
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:16
    References:45
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