English

Some homological criteria for regular, complete intersection and Gorenstein rings

Commutative Algebra 2013-02-25 v2 K-Theory and Homology

Abstract

Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field (Serre, Avramov, Auslander). It is also known that in positive characteristic, the Frobenius endomorphism can also be used for these characterizations (Kunz, ...), and more generally any contracting endomorphism. We introduce here a class of local homomorphisms, in some sense larger than all above, for which these characterizations still hold, providing an unified treatment for this class of homomorphisms.

Keywords

Cite

@article{arxiv.1209.5051,
  title  = {Some homological criteria for regular, complete intersection and Gorenstein rings},
  author = {Javier Majadas},
  journal= {arXiv preprint arXiv:1209.5051},
  year   = {2013}
}

Comments

v2: some parts have been rewritten, a minor mistake corrected, Remark 9 and some references added; all the results remain unchanged