Geodesic
On the Group $GL(2,K[t])$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 321-327

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The group mentioned in the title of the paper is one of the simplest examples of infinite-dimensional algebraic groups. In this paper, an increasing sequence of finite-dimensional schemes is constructed that exhausts this group. It is proved that these schemes are reduced and irreducible and are complete intersections. The set of singular points of these schemes is obtained. 
@article{TM_2004_246_a22,
     author = {I. R. Shafarevich},
     title = {On the {Group} $GL(2,K[t])$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {321--327},
     publisher = {mathdoc},
     volume = {246},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_246_a22/}
}
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I. R. Shafarevich. On the Group $GL(2,K[t])$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 321-327. http://geodesic.mathdoc.fr/item/TM_2004_246_a22/