Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
@article{bwmeta1.element.doi-10_2478_BF02475667,
author = {Stanis\l aw Kasjan},
title = {Representation-finite triangular algebras form an open scheme},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {97-107},
zbl = {1063.16022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475667}
}
Stanisław Kasjan. Representation-finite triangular algebras form an open scheme. Open Mathematics, Tome 1 (2003) pp. 97-107. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475667/
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