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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 19 > No. 2

 
   

On Microlocalization of Graded and Filtered Formal Modules

PP: 245-249
doi:10.18576/amis/190201
Author(s)
Nawal M. NourEldeen, A. E. Radwan, Ahmed Aboubakr,
Abstract
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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