Abstract
There are some elementary theorems on geometry over a non algebraically closed field. For Example: 1. Every set of k-rational points of a projective variety is homeomorphic to the maximal spectrum of some k-algebra. 2. A properly defined real divisor class group of normal ℝ-variety is a ℤ/2-vectorspace.
In this paper we obtain generalizations which say: The hypothesis, that a fixed polynomial has no zero modulo some prime ideals, has strong conclusions.
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Ischebeck, F. Binäre Formen und Primideale. Manuscripta Math 35, 147–163 (1981). https://doi.org/10.1007/BF01168453
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DOI: https://doi.org/10.1007/BF01168453