Homological criteria for regular homomorphisms and for locally complete intersection homomorphisms

@inproceedings{Avramov2000HomologicalCF,
title={Homological criteria for regular homomorphisms and for locally complete intersection homomorphisms},
author={Luchezar L. Avramov and Srikanth B. Iyengar},
year={2000}
}

Regularity and complete intersection are properties of commutative noetherian rings, motivated by geometry, but often best approached through homological methods. For an illustration, it suffices to recall that no non-homological proof is known for the stability of these properties under such a basic operation as localization. It has long been known that ‘nice’ algebras have ‘simple’ homology. For flat algebras of finite type a famous example is provided by Hochschild, Kostant, and Rosenberg… CONTINUE READING