by Yanagawa, Kohji

Let $E = K{\left\langle {y_{1} ,…,y_{n} } \right\rangle }$ be the exterior algebra. The (cohomological) distinguished pairs of a graded E-module N describe the growth of a minimal graded injective resolution of N. Römer gave a duality theorem between the distinguished pairs of N and those of its dual N
*. In this paper, we show that under Bernstein–Gel’fand–Gel’fand correspondence, his theorem is translated into a natural corollary of local duality for (complexes of) graded $S=K[x_1, \ldots, x_n]$-modules. Using this idea, we also give a $\mathbb{Z}^{n} $-graded version of Römer’s theorem.

DOI: 10.1007/s10468-006-9037-y
Online Date: 9/14/2006
Print publication date: 12/1/2006
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