## Abstract

Let * R * → * S * be a homomorphism of rings and let * M * be a finitely generated * S * -module. Then the finitely generated * R * -module * L * is called a * lifting * of * M * to * R * if * M * ≅ * S * ⊗ _{ R } * L * and Tor ^{ R } _{ i } ( * S * , * L * )=0 for all integers * i * >0. The * S * -module * M * is said to be * liftable * to * R * , when such an * R * -module * L * exists.

Let * S * be a Noetherian * R * -algebra where ( * R * , ** m ** ) is a commutative local ring, ** x ** = * x * _{ 1 } …, * x * _{ n } be an * S * -regular sequence in ** m ** and * T * = * S * / ** x ** * S * . Auslander, Ding and Solberg proved that if * M * is a finitely generated * T * -module with Ext ^{ 2 } _{ T } ( * M * , * M * )=0, then * M * is liftable to * S * . Furthermore, if * N * is a finitely generated * T * -module which is liftable to * S * and Ext ^{ 1 } _{ T } ( * N * , * N * )=0, then the lifting of * N * to * S * is unique.

In this talk, we are mainly concerned with the generalizations of these results for DG algebras. In particular, we investigate lifting properties for semifree DG-modules over Koszul complexes. We apply DG algebra techniques to study lifting of modules and complexes from the Koszul complexes over some elements contained in the maximal ideal of commutative complete local ring to the ring itself.

Original language | American English |
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State | Published - Mar 20 2011 |

Event | Special Session on Commutative Ring Theory, Spring Central Section Meeting of the American Mathematical Society, University of Iowa - Duration: Mar 20 2011 → … |

### Conference

Conference | Special Session on Commutative Ring Theory, Spring Central Section Meeting of the American Mathematical Society, University of Iowa |
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Period | 03/20/11 → … |

## Keywords

- Commutative local ring
- Complete local ring
- DG algebras
- DG modules
- Homomorphism rigns
- Koszul complex
- Lifting
- Lifting properties
- Noetherian algebra

## DC Disciplines

- Mathematics