On asymptotic socle degrees of local cohomology modules

Abstract

Let R be a standard graded algebra over a field k and I be a homogeneous ideal of R . We study the question whether there is a constant c such that Soc ( H m j ( R / I t ) ) < − c t = 0 for all t ≥ 1 and a variation of this question. We also draw a connection between this question and the notion of gauge-boundedness in prime characteristic.