Function Field (scheme Theory)
The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U. Despite its name, KX does not always give a field for a general scheme X.
Read more about Function Field (scheme Theory): Simple Cases, General Case, Further Issues, Bibliography
Famous quotes containing the words function and/or field:
“Any translation which intends to perform a transmitting function cannot transmit anything but information—hence, something inessential. This is the hallmark of bad translations.”
—Walter Benjamin (1892–1940)
“Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.”
—Sara Lawrence Lightfoot (20th century)