Loading [MathJax]/extensions/tex2jax.js

The Stacks project

Proposition 64.8.2. In the situation above, we have

\[ \text{gr}^ p \circ RT = RT \circ \text{gr}^ p \]

where the $RT$ on the left is the filtered derived functor while the one on the right is the total derived functor. That is, there is a commuting diagram

\[ \xymatrix{ DF^+(\mathcal{A}) \ar[r]^{RT} \ar[d]_{\text{gr}^ p} & DF^+(\mathcal{B}) \ar[d]^{\text{gr}^ p}\\ D^+(\mathcal{A}) \ar[r]^{RT} & D^+(\mathcal{B}).} \]

Proof. Omitted. $\square$


Comments (0)


Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.