The finite type of modules of bounded projective dimension and Serre's conditions

Autor:	Hrbek, Michal, Gros, Giovanna Le
Rok vydání:	2023
Předmět:	Mathematics - Commutative Algebra Mathematics - Rings and Algebras 13C05 13D07 13C60 16E65
Druh dokumentu:	Working Paper
Popis:	Let $R$ be a commutative noetherian ring. We prove that the class of modules of projective dimension bounded by $k$ is of finite type if and only if $R$ satisfies Serre's condition $(S_k)$. In particular, this answers positively a question of Bazzoni and Herbera in the specific setting of a Gorenstein ring. Applying similar techniques, we also show that the $k$-dimensional version of the Govorov-Lazard Theorem holds if and only if $R$ satisfies the "almost" Serre condition $(C_{k+1})$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.14346 Zobrazit plný text záznamu View this record from Arxiv