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The function field of an irreducible classical affine variety
Definition
Let be a classical affine variety. Since A classical affine variety has a domain as its coordinate ring, and conversely shows that is an integral domain, its field of fractions exists.
The function field of is
Depends on
Used by
- A rational function is regular at a point exactly when it lies in the local ring Definition
- Dominant maps pull back function fields functorially Lemma
- All nonempty affine opens of an irreducible affine variety have the same function field Theorem
- Dominant rational maps to an affine variety correspond to injective homomorphisms of function fields Theorem
Dependency tree · two levels
8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Donu Arapura, Notes on Basic Algebraic Geometry, §3.1 (standard reference, not scraped)
- Michael Artin, Notes for a Course in Algebraic Geometry, Definition 3.4.3 (standard reference, not scraped)