Function field

Encyclopedia

**Function field**may refer to:

- Function field of an algebraic varietyFunction field of an algebraic varietyIn algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V...
- Function field (scheme theory)Function field (scheme theory)In algebraic geometry, the function field KX of a scheme Xis a generalization of the notion of a sheaf of rational functions on a variety. 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 is the set of...