Definition 76.52.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ which is flat and locally of finite presentation. An object $E$ of $D(\mathcal{O}_ X)$ is perfect relative to $Y$ or $Y$-perfect if $E$ is pseudo-coherent (Cohomology on Sites, Definition 21.45.1) and $E$ locally has finite tor dimension as an object of $D(f^{-1}\mathcal{O}_ Y)$ (Cohomology on Sites, Definition 21.46.1).
Post a comment
Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)