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:
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“The snow had begun in the gloaming,
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—James Russell Lowell (1819–1891)