5 problems

Let $(R,\mathfrak{m})$ be a regular local ring of dimension $n$. Let $I$ be an ideal generated by an $R$-regular sequence of length $k\leq n-1$, and let $J$ be an ideal generated b…

Let $(R,\mathfrak{m})$ be a regular local ring of dimension $n$. Let $I$ be an ideal generated by an $R$-regular sequence of length $k\leq n$, and let $J$ be an ideal generated by…

Let $R$ be a regular local ring of dimension $n$, let $I$ be an ideal in $R$ generated by a regular sequence of length $k\le n$, and let $J$ be an ideal in $R$ generated by a regul…

Rigidity conjecture for Tor. If

Weak Horrocks conjecture. One has