Assertion: topological curve | /r/HasProperty | equivalent
Facets:
value: over f.
type: OTHER
value: categorically
type: DEGREE
value: up to birational equivalence
type: OTHER
Source sentences:
text: Up to birational equivalence, the irreducible curves over a field F are categorically equivalent to algebraic function fields in one variable over F. Such an algebraic function field is a field extension K of F that contains an element x which is transcendental over F, and such that K is a finite algebraic extension of F(x), which is the field of rational functions in the indeterminate x over F.