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Sequence-regular commutative DG-rings.
- Source :
-
Journal of Algebra . Jun2024, Vol. 647, p400-435. 36p. - Publication Year :
- 2024
-
Abstract
- We introduce a new class of commutative noetherian DG-rings which generalizes the class of regular local rings. These are defined to be local DG-rings (A , m ¯) such that the maximal ideal m ¯ ⊆ H 0 (A) can be generated by an A -regular sequence. We call these DG-rings sequence-regular DG-rings, and make a detailed study of them. Using methods of Cohen-Macaulay differential graded algebra, we prove that the Auslander-Buchsbaum-Serre theorem about localization generalizes to this setting. This allows us to define global sequence-regular DG-rings, and to introduce this regularity condition to derived algebraic geometry. It is shown that these DG-rings share many properties of classical regular local rings, and in particular we are able to construct canonical residue DG-fields in this context. Finally, we show that sequence-regular DG-rings are ubiquitous, and in particular, any eventually coconnective derived algebraic variety over a perfect field is generically sequence-regular. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRAIC geometry
*DIFFERENTIAL algebra
*LOCAL rings (Algebra)
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 647
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 176296826
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2024.02.034