Abstract.
Let R be a complete local ring of dimension d over a perfect field of prime characteristic p, and let M be an R-module of finite length and finite projective dimension. S. Dutta showed that the equality \(\lim_{n\to\infty}\frac{\ell(F^n_R(M))}{p^{nd}} = \ell(M)\) holds when the ring R is a complete intersection or a Gorenstein ring of dimension at most 3. We construct a module over a Gorenstein ring R of dimension five for which this equality fails to hold. This then provides an example of a nonzero Todd class \(\tau_3(R)\), and of a bounded free complex whose local Chern character does not vanish on this class.
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Received: February 11, 1999
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Miller, C., Singh, A. Intersection multiplicities over Gorenstein rings. Math Ann 317, 155–171 (2000). https://doi.org/10.1007/s002080050362
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DOI: https://doi.org/10.1007/s002080050362