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. 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.
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.
Read more about Formal Scheme: Definition, Morphisms Between Formal Schemes, See Also
Famous quotes containing the words formal and/or scheme:
“On every formal visit a child ought to be of the party, by way of provision for discourse.”
—Jane Austen (1775–1817)
“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)