Proregular sequences, local cohomology, and completion

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On Gorenstein projective, injective and flat dimensions—A functorial description with applications (2004, methodology): “For local cohomology this representation goes back to Grothendieck [28, Proposition 1.4.1]; see also [1, Lemma 3.1.1] and the corrections in [42, Section 1].”
Abelian right perpendicular subcategories in module categories (2017, background): “ to certain (sets of) modules of projective dimension not exceeding 1. The latter results depend on Noetherianity assumptions. These can be weakened to weak proregularity assumptions (in the sense of [37, 22, 27]), and somewhat further, as we show in this paper. On the other hand, we demonstrate an ”
Local duality in algebra and topology (2015, background): “degree zero. It is then natural to ask when ΓI is in fact the total right derived functor of the I-power torsion functor TIdeﬁned at the abelian level. A complete answer to this question was given in [Sch03]. First, we recall the following deﬁnition. Deﬁnition 3.14. An ideal Iis generated by a weakl”
On formal local cohomology and connectedness (2007, methodology): “[4, Section 19], [15] and [20]) the Mayer-Vietoris sequence in local cohomology is an important tool for connectedness phenomenons.”