Rigid-Analytic Artin-Grothendieck Vanishing

In this paper, we address two conjectures about the rigid-analytical analogues of the Artin--Grothendieck Vanishing Theorem. First, we show the remaining cases of the Artin--Grothendieck Vanishing Theorem for affinoid algebras, which was previously considered in Section 7 of [BM21]. Second, we prove a stronger version of the rigid-analytic Artin--Grothendieck Vanishing Conjecture (see Conjecture 1.2 in [Han20]) over a field of characteristic 0, and a weaker version over a field of characteristic p>0.