9 problems

Core formula conjecture. The core of $I$ should satisfy

Let $R$ be a Cohen–Macaulay ring, let $I$ be an ideal of $R$, and let $\mathfrak{a}$ be an ideal such that … is an $s$-residual intersection. Write…

Residual-intersection conjecture. If $I$ is unmixed and $J:I$ is a geometric $(\ell-1)$-residual intersection of $I$, then, for all $\rho\gg0$,

Let $R$ be a Cohen–Macaulay ring, let $\mathfrak a\subseteq I$ be ideals, and write … Assume that $J$ is an algebraic $s$-residual intersection. The Kitt ideal…

Let $R$ be a Cohen–Macaulay local ring of dimension $d$, let $I$ be an ideal satisfying sliding depth, and let $s$ be the residual-intersection parameter. An algebraic $s$-residual…

Let $R$ be a commutative ring, let $I$ be an ideal with sliding depth, and let $J=\mathfrak a:_R I$ be an algebraic $s$-residual intersection. A disguised residual intersection is…

Let $R$ be a Cohen–Macaulay local or $^*\!$local ring, and let $I$ be a strongly Cohen–Macaulay ideal, or more generally an ideal satisfying sliding depth. Let…

Let $A$ be a nonsingular variety, let $X\subset A$ be a closed subscheme, and let $Y$ be a general $t$-residual intersection of $X$ in the sense of the paper. The singularities MJ-…

Let $(R,\mathfrak{m})$ be a Cohen–Macaulay local ring of dimension $d$, let $I$ be an ideal satisfying the sliding depth condition, and let $\mathfrak{a}\subseteq I$ define an alge…