A FREENESS CRITERION WITHOUT PATCHING FOR MODULES OVER LOCAL RINGS

Autor:	Sylvain Brochard, Srikanth B. Iyengar, Chandrashekhar B. Khare
Rok vydání:	2021
Předmět:	Mathematics - Number Theory General Mathematics FOS: Mathematics ComputingMethodologies_DOCUMENTANDTEXTPROCESSING 13C10 (primary) 13D02 11F80 (secondary) Number Theory (math.NT) Commutative Algebra (math.AC) Mathematics - Commutative Algebra
Zdroj:	Journal of the Institute of Mathematics of Jussieu. :1-13
ISSN:	1475-3030 1474-7480
Popis:	It is proved that if $\varphi\colon A\to B$ is a local homomorphism of commutative noetherian local rings, a nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ is at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, is free over $B$, and $\varphi$ is a special type of complete intersection. This result is motivated by a "patching method" developed by Taylor and Wiles, and a conjecture of de Smit, proved by the first author, dealing with the special case when $N$ is flat over $A$. Comment: 11 page; minor changes in version 2. To appear in J. Inst. Math. Jussieu
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5a651036ca61124b5ae1acfea6c564d https://doi.org/10.1017/s147474802100061x Zobrazit plný text záznamu