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On Microlocalization of Graded and Filtered Formal Modules |
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PP: 245-249 |
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doi:10.18576/amis/190201
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Author(s) |
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Nawal M. NourEldeen,
A. E. Radwan,
Ahmed Aboubakr,
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Abstract |
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| We modify and generalize the basic theory of formal completion ($I$-adic completion) as in \cite{3}, \cite{8} and \cite{6} with using a general Zariskian filtration $\mathcal{F}\mathcal{R}$ and replacing quiotient filtration $\mathcal{F}\left(\frac{\mathcal{R}}{{I}^{n}}\right)$; $n\in \mathcal{Z}$. We establish the exactness, finitness and flatness of formal completion. The formal microlocalization of ${\mathcal{R}}^{\mathrm{\wedge}I}$-module ${\mathcal{M}}^{\mathrm{\wedge}I}$ represents the solution of formal schemes studied on the filtered level in [10], [9] and [11]. |
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