Homological Algebra Modulo a Regular Sequence with Special Attention to Codimension Two
Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological properties M over R and over Q are intimately related. Their links are analyzed here from the point of view of differential graded homological algebra...
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| Vydáno v: | Journal of algebra Ročník 230; číslo 1; s. 24 - 67 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Inc
01.08.2000
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| ISSN: | 0021-8693, 1090-266X |
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| Abstract | Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological properties M over R and over Q are intimately related. Their links are analyzed here from the point of view of differential graded homological algebra over a Koszul complex that resolves R over Q. One outcome of this approach is a transparent derivation of some central results of the theory. Another is a new insight into codimension two phenomena, yielding an explicit finitistic construction of the generally infinite minimal R-free resolution of M. It leads to theorems on the structure and classification of finite modules over codimension two local complete intersections that are exact counterparts of Eisenbud's results for modules over hypersurfaces. |
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| AbstractList | Let M be a finite module over a ring R obtained from a commutative ring Q by factoring out an ideal generated by a regular sequence. The homological properties M over R and over Q are intimately related. Their links are analyzed here from the point of view of differential graded homological algebra over a Koszul complex that resolves R over Q. One outcome of this approach is a transparent derivation of some central results of the theory. Another is a new insight into codimension two phenomena, yielding an explicit finitistic construction of the generally infinite minimal R-free resolution of M. It leads to theorems on the structure and classification of finite modules over codimension two local complete intersections that are exact counterparts of Eisenbud's results for modules over hypersurfaces. |
| Author | Avramov, Luchezar L Buchweitz, Ragnar-Olaf |
| Author_xml | – sequence: 1 givenname: Luchezar L surname: Avramov fullname: Avramov, Luchezar L organization: Department of Mathematics, Purdue University, West Lafayette, IN, 47907, f1avramov@math.purdue.eduf1 – sequence: 2 givenname: Ragnar-Olaf surname: Buchweitz fullname: Buchweitz, Ragnar-Olaf organization: Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, Canadaf2ragnar@math.utoronto.caf2 |
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| Cites_doi | 10.1017/S0305004100031960 10.1090/S0002-9947-1980-0570778-7 10.7146/math.scand.a-11518 10.1215/ijm/1255378502 10.1006/jabr.1997.7317 10.1073/pnas.42.1.36 10.1016/0021-8693(69)90023-4 10.1007/BF02698901 10.1016/0022-4049(94)90134-1 10.1016/0001-8708(75)90046-8 10.2307/1970159 10.1017/S0027763000001264 10.1016/0022-4049(91)90081-C 10.1090/S0002-9947-1957-0086822-7 10.1016/0021-8693(89)90244-5 10.1007/BF01393971 10.1017/S0305004100031650 10.1090/S0002-9947-1972-0306192-4 10.1215/ijm/1255629829 10.1006/jabr.1996.6901 10.2307/2374187 10.2307/2373926 10.24033/bsmf.1380 |
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