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張茗遠 ( National Taiwan University )
2022-08-23  14:00 - 16:00
Room 201, Astronomy and Mathematics Building

To collect infinitesimal information of the surroundings of a closed subscheme, we introduce the concept of formal schemes by completion. We will define similar concepts such as affine formal schemes and coherent sheaves, and show some basic properties.
Next, we will show the method to reverse the construction and obtain original schemes from the formal scheme, using the concept of “ideal of definition”.
Finally, we will investigate the connection between original schemes and formal schemes, especially the connection of coherent sheaves.