Wiles defect for modules and criteria for freeness

2021/07/14 by Brochard, Sylvain, Iyengar, Srikanth B., Khare, Chandrashekhar B.
#11F80 (primary) #13C99 #13F99 (secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.06759

Abstract

F. Diamond proved a numerical criterion for modules over local rings to be free modules over complete intersection rings. We formulate a refinement of these results using the notion of Wiles defect. A key step in the proof is a formula that expresses the Wiles defect of a module in terms of the Wiles defect of the underlying ring.

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