2 problems

Let $(R,\mathfrak{m},\mathbb{K})$ be a commutative Noetherian local ring with residue field $\mathbb{K}=R/\mathfrak{m}$, let $I\subset R$ be an ideal, and let $H_I^j(R)$ denote the…

Hellus's conjecture. If $\operatorname{H}^i_I(R)\neq 0$, then