Abstract
Let I denote an ideal of a local Gorenstein ring \({(R, \mathfrak m)}\) . Then we show that the local cohomology module \({H^c_I(R)}\) , c = height I, is indecomposable if and only if V(I d ) is connected in codimension one. Here I d denotes the intersection of the highest dimensional primary components of I. This is a partial extension of a result shown by Hochster and Huneke in the case I the maximal ideal. Moreover there is an analysis of connectedness properties in relation to various aspects of local cohomology. Among others we show that the endomorphism ring of \({H^c_I(R)}\) is a local Noetherian ring if dim R/I = 1.
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Schenzel, P. On connectedness and indecomposibility of local cohomology modules. manuscripta math. 128, 315–327 (2009). https://doi.org/10.1007/s00229-008-0229-0
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DOI: https://doi.org/10.1007/s00229-008-0229-0