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have unique generic and special points, but a more complicated spectrum, since they represent general dimensions. The discrete valuation case is much like the complex
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In the rapid foundational changes of the 1950s Weil's approach became obsolete. In
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This was at a cost of there being a huge collection of equally generic points.
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over the field generated by the coefficients of the equations of the variety.
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519:. Cambridge Tracts in Theoretic Computer Science. Vol. 5. p. 65.
538:. American Mathematical Society Colloquium Publications. Vol. XXIX.
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is a point such that the field generated by its coordinates has
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are true, a generic property being a property which is true for
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is the whole spectrum, the definition has been extended to
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approach to algebraic geometry, popular in the 1930s).
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In classical algebraic geometry, a generic point of an
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434:), the fiber above the special point is the
248:The terminology arises from the case of the
446:and other theories about degeneration. The
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438:, an important concept for example in
484:The Red Book of Varieties and Schemes
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47:adding citations to reliable sources
379:and Zariski thinks in terms of the
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536:Foundations of Algebraic Geometry
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332:were a whole class of points of
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16:Concept in algebraic geometry
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481:(2005) . "II Preschemes".
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487:. Springer. p. 67.
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422:coming from the unique
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43:improve this article
426:. For morphisms to
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336:taking values in a
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517:Topology via Logic
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394:. For example for
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307:André Weil
233:is all of
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268:Examples
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301:History
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