function field of an algebraic varietyの例文

例文

1. This is typically the case for algebraic geometry over a field of prime characteristic, where the function field of an algebraic variety has a transcendence degree over the ground field that is equal to the dimension of the variety.
2. Except when the base field is the field of rational numbers or an imaginary quadratic field, the abelian Stark conjectures are still unproved in number fields, and more progress has been made in function fields of an algebraic variety.
3. There the function field of an algebraic variety " V " is formed as the field of fractions of the coordinate ring of " V " ( more accurately said, of a Zariski-dense affine open set in " V " ).
4. In 1944 Oscar Zariski defined an abstract Zariski Riemann space from the function field of an algebraic variety, for the needs of birational geometry : this is like a direct limit of ordinary varieties ( under'blowing up'), and the construction, reminiscent of locale theory, used valuation rings as points.