Geodesic
Construction of a~linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$
Sbornik. Mathematics, Tome 208 (2017) no. 4, pp. 568-584

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

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, reduction.
Mots-clés : filtration 
@article{SM_2017_208_4_a5,
     author = {A. L. Smirnov and S. S. Yakovenko},
     title = {Construction of a~linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$},
     journal = {Sbornik. Mathematics},
     pages = {568--584},
     publisher = {mathdoc},
     volume = {208},
     number = {4},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_4_a5/}
}
TY  - JOUR
AU  - A. L. Smirnov
AU  - S. S. Yakovenko
TI  - Construction of a~linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$
JO  - Sbornik. Mathematics
PY  - 2017
SP  - 568
EP  - 584
VL  - 208
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2017_208_4_a5/
LA  - en
ID  - SM_2017_208_4_a5
ER  - 
%0 Journal Article
%A A. L. Smirnov
%A S. S. Yakovenko
%T Construction of a~linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$
%J Sbornik. Mathematics
%D 2017
%P 568-584
%V 208
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2017_208_4_a5/
%G en
%F SM_2017_208_4_a5
A. L. Smirnov; S. S. Yakovenko. Construction of a~linear filtration for bundles of rank $2$ on $\mathbf{P}^1_{\mathbb Z}$. Sbornik. Mathematics, Tome 208 (2017) no. 4, pp. 568-584. http://geodesic.mathdoc.fr/item/SM_2017_208_4_a5/