Cohomology of Finite Modules over Short Gorenstein Rings
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Abstract
We study two formal power series in the indeterminate t that generalize the Poincar´e series of a module. In the context of a Gorenstein local ring whose maximal ideal m satisfies m³ = 0, we prove that these two power series are rational functions of t. Moreover, the denominators of these two power series are shown to be the same as the denominator of the Poincaré series in this class of rings.
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Introduction -- Background -- The main theorem -- Complete intersection rings -- Concluding comments
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Ph.D.