Lemma 20.44.6. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $(K, L, M, f, g, h)$ be a distinguished triangle in $D(\mathcal{O}_ X)$. Let $a, b \in \mathbf{Z}$.

If $K$ has tor-amplitude in $[a + 1, b + 1]$ and $L$ has tor-amplitude in $[a, b]$ then $M$ has tor-amplitude in $[a, b]$.

If $K$ and $M$ have tor-amplitude in $[a, b]$, then $L$ has tor-amplitude in $[a, b]$.

If $L$ has tor-amplitude in $[a + 1, b + 1]$ and $M$ has tor-amplitude in $[a, b]$, then $K$ has tor-amplitude in $[a + 1, b + 1]$.

## Comments (0)