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A FREENESS CRITERION WITHOUT PATCHING FOR MODULES OVER LOCAL RINGS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 5 / September 2023
- Published online by Cambridge University Press:
- 20 December 2021, pp. 2117-2129
- Print publication:
- September 2023
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- Article
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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 
$\operatorname {edim} A - \operatorname {edim} B$ 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.
