Graded Complexes Over Power Series Rings
Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 158-178
Voir la notice de l'article provenant de la source Cambridge University Press
A common method in studying a commutative Noetherian local ring A is to find a regular subring R contained in A so that A becomes a finitely generated R-module, and in this way one can obtain some information about the original ring by applying what is known about regular local rings. By the structure theorems of Cohen, if A is complete and contains a field, there will always exist such a subring R, and R will be a power series ring k[[X 1, ..., Xn ]] = k[[X]] over a field k. In this paper we show that if R is chosen properly, the ring A (or, more generally, an A-module M), will have a comparatively simple structure as an R-module. More precisely, A (or M) will have a free resolution which resembles the Koszul complex on the variables (X 1, ..., Xn ) = (X); such a complex will be called an (X)-graded complex and will be given a precise definition below.
Roberts, Paul. Graded Complexes Over Power Series Rings. Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 158-178. doi: 10.4153/CJM-1986-008-8
@article{10_4153_CJM_1986_008_8,
author = {Roberts, Paul},
title = {Graded {Complexes} {Over} {Power} {Series} {Rings}},
journal = {Canadian journal of mathematics},
pages = {158--178},
year = {1986},
volume = {38},
number = {1},
doi = {10.4153/CJM-1986-008-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-008-8/}
}
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