Minimaxness and finiteness properties of formal local cohomology modules (Q493158)

Formal local cohomology modules were introduced by \textit{P. Schenzel} [J. Algebra 315, No. 2, 894--923 (2007; Zbl 1131.13018)]. Let \((R, \mathfrak m)\) be a Noetherian local ring, \(\mathfrak a \subset R\) an ideal and \(M\) a finitely generated \(R\)-module. The \(i\)th formal local cohomology module of \(M\) with respect to \(\mathfrak a\) is defined to be \(\mathfrak F^i_{\mathfrak a}(M) = \varprojlim_n H_{\mathfrak m}^i(M/\mathfrak a^n M)\). Schenzel also computed \(\sup\{i \mid \mathfrak F^i_{\mathfrak a}(M) \neq 0\}\) and \(\inf\{i \mid \mathfrak F^i_{\mathfrak a}(M) \neq 0\}\). In the present paper, the author compute invariants above in which ``\(\neq 0\)'' is replaced by ``is finitely generated'' or ``is minimal.''