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Article Dans Une Revue Journal of the Institute of Mathematics of Jussieu Année : 2021

A FREENESS CRITERION WITHOUT PATCHING FOR MODULES OVER LOCAL RINGS

Résumé

Abstract 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 .
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Dates et versions

hal-03544389 , version 1 (26-01-2022)

Identifiants

Citer

Sylvain Brochard, Srikanth B Iyengar, Chandrashekhar B Khare. A FREENESS CRITERION WITHOUT PATCHING FOR MODULES OVER LOCAL RINGS. Journal of the Institute of Mathematics of Jussieu, In press, 22 (5), pp.2117 - 2129. ⟨10.1017/S147474802100061X⟩. ⟨hal-03544389⟩
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