The signature of the chern coefficients of local rings

This paper considers the following conjecture: If R is an unmixed, equidimensionallocal ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived. © International Press 2009.

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