Localization at countably infinitely many prime ideals and applications (Q2797000)

In the present paper, authors gave a good flat morphism between Noetherian rings. That is, let \(R\) be a Noetherian ring and \(\mathfrak p_1\), \(\mathfrak p_2\), \dots\ are countably many prime ideals such that \(\mathfrak p_i \not\subset \mathfrak p_j\) whenever \(i \neq j\). Then there is a flat \(R\)-algebra \(S\) such that \(\mathfrak p_1 S\), \(\mathfrak p_2 S\), \dots\ are all the maximal ideals of \(S\).NEWLINENEWLINEAuthors used it to study associated primes of local cohomology modules. Let \(R\) be a Noetherian ring, \(I\) an ideal and \(M\) a finitely generated \(R\)-module. It is not known whether \(\text{Ass} H_I^i(M)\) is a finite set. However they showed that \(\# \{\mathfrak p \in \text{Ass} H_I^i(M) \mid \text{ht} \mathfrak p/I \leq 1\} < \infty\).