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

• Victor H. Jorge-Pérez ^[1] ; Cleto B. Miranda-Neto ^[2]
  1. [1] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
  2. [2] Universidade Federal da Paraíba

     Universidade Federal da Paraíba

     Brasil

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 2, 2022, págs. 203-219
• Idioma: inglés
• DOI: 10.1007/s13348-021-00314-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let R be a Noetherian local k-algebra whose derivation module {\mathrm{Der}}_k(R) is finitely generated. Our main goal in this paper is to investigate the impact of assuming that {\mathrm{Der}}_k(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 {\mathrm{depth}}\,R=3 of the Herzog–Vasconcelos conjecture and consequently to the strong version of the Zariski–Lipman conjecture.