High Quality Content by WIKIPEDIA articles! In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. Formal schemes are usually defined only in the Noetherian case. While there have been several definitions of non-Noetherian formal schemes, these encounter technical problems. Consequently we will make the assumption that all rings are Noetherian.

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