## Une caract?risation de la surcoh?rence

J. Math. Sci. Univ. Tokyo
Vol. 16 (2009), No. 1, Page 1--21.

Caro, Daniel
Une caract?risation de la surcoh?rence
Let $\mathcal{P}$ be a proper smooth formal $\mathcal{V}$-scheme, $\mathcal{E} \in F\text{-}D ^\mathrm{b} _\mathrm{coh} ( \D ^\dag _{\mathcal{P},\mathbb{Q}})$. We check that $\mathcal{E}$ is $\D ^\dag _{\mathcal{P},\mathbb{Q}}$-overcoherent if and only if, for any morphism $f\,:\, \mathcal{P}' \rightarrow \mathcal{P}$ of smooth formal $\mathcal{V}$-schemes, $f ^! (\mathcal{E})$ is $\D ^\dag _{\mathcal{P}', \, \mathbb{Q}}$-coherent.