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
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Abstract:
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.

Mathematics Subject Classification (2000): 14F30, 14F40
Mathematical Reviews Number: MR2548931

Received: 2008-06-17