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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
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

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

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