Resumen de Homological aspects of derivation modules and critical case of the Herzog–Vasconcelos conjecture

V. H. Jorge Pérez, Cleto B. Miranda Neto

• Let R be a Noetherian local k-algebra whose derivation module Derk(R) is finitely generated. Our main goal in this paper is to investigate the impact of assuming that Derk(R) has finite projective dimension (or finite Gorenstein dimension), mainly in connection with freeness, under a suitable hypothesis concerning the vanishing of (co)homology or the depth of a certain tensor product. We then apply some of our results towards the critical case depthR=3 of the Herzog–Vasconcelos conjecture and consequently to the strong version of the Zariski–Lipman conjecture.