Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.
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机译：令C为在Laurent多项式环L = R [x，x-1，y，y-1]上有限生成的自由模的有界共链复数。如果复数C在R上等于同态，则称为R有限控制。我们的主要结果是用Novikov同调性来刻画R有限控制的复合物的特征：当且仅当从C衍生的8个复合物是非循环的时，C才是R有限控制的。这些络合物是C⊗LR[[x，y]] [（xy）-1]和C⊗LR[x，x-1] [[y]] [y-1]，以及通过交换x和y获得的变体，并用其反数代替不确定的数。
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