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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
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.
Received: 04.07.2016 and 02.11.2016
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
Linking options:
https://www.mathnet.ru/eng/sm8775https://doi.org/10.1070/SM8775 https://www.mathnet.ru/eng/sm/v208/i4/p111
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Abstract page: | 538 | Russian version PDF: | 83 | English version PDF: | 16 | References: | 45 | First page: | 16 |
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