http://wiki.karljones.com/index.php?action=history&feed=atom&title=Formal_scheme 2026-10-23T17:46:13Z Revision history for this page on the wiki MediaWiki 1.24.2 http://wiki.karljones.com/index.php?title=Formal_scheme&diff=19766&oldid=prev 2016-12-01T19:39:49Z

<p>Created page with &quot;In <a href="/index.php/Mathematics" title="Mathematics">mathematics</a>, specifically in <a href="/index.php/Algebraic_geometry" title="Algebraic geometry">algebraic geometry</a>, a &#039;&#039;&#039;formal scheme&#039;&#039;&#039; is a type of <a href="/index.php/Space_(mathematics)" title="Space (mathematics)">Space (mathematics)</a> space which includes data about its surroundings. == De...&quot;</p> <p><b>New page</b></p><div>In [[mathematics]], specifically in [[algebraic geometry]], a '''formal scheme''' is a type of [[Space (mathematics)]] space which includes data about its surroundings.<br /> <br /> == Description ==<br /> <br /> Unlike an ordinary [[Scheme (mathematics)|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. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.<br /> <br /> A locally [[noetherian]] scheme is a locally noetherian formal scheme in the canonical way: the formal completion along itself. In other words, the category of locally noetherian formal schemes contains all locally noetherian schemes.<br /> <br /> == See also ==<br /> <br /> * [[Algebraic geometry]]<br /> * [[Noetherian scheme]]<br /> * [[Scheme (mathematics)]]<br /> * [[Space (mathematics)]]<br /> <br /> == External links ==<br /> <br /> * [https://en.wikipedia.org/wiki/Formal_scheme Formal scheme] @ Wikipedia<br /> <br /> [[Category:Mathematics]]</div>

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