WebThe class of Hilbertian fields contains, for example, algebraic number fields and finitely generated transcendental extensions of arbitrary fields [5, Theorem 13.4.2]. Corollary 3.8. Let K be a Hilbertian field or a finite field and let S be a numerical monoid. Then
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WebField Arithmetic pp 219–230Cite as. Home. Field Arithmetic. Chapter. Hilbertian Fields Hilbertian Fields. Chapter; 2156 Accesses. Part ... Hilbertian Fields. In: Field Arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 11. WebA field F is called Hilbertian if the following property holds: If f(t, x) e F[x, t] is an irreducible polynomial then there are infinitely many ae F such that the specialization f(a, x) is irreducible as a polynomial in F[x]. To state this property in other language, let Pa = (t - a) ç F[t] be the prime ideal. tim grey gear
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WebHilbertian Field; These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. ... K. Uchida, Separably Hilbertian fields, Kodai Mathematical Journal 3 (1980), 83–95. CrossRef MathSciNet MATH Google Scholar Download references. Author … A Hilbertian variety V over K is one for which V(K) is not thin: this is a birational invariant of V. A Hilbertian field K is one for which there exists a Hilbertian variety of positive dimension over K: the term was introduced by Lang in 1962. If K is Hilbertian then the projective line over K is Hilbertian, so this may be taken … See more In mathematics, a thin set in the sense of Serre, named after Jean-Pierre Serre, is a certain kind of subset constructed in algebraic geometry over a given field K, by allowed operations that are in a definite sense 'unlikely'. The … See more More precisely, let V be an algebraic variety over K (assumptions here are: V is an irreducible set, a quasi-projective variety, and K has characteristic zero). A type I thin set is a subset of … See more The WWA property (weak 'weak approximation', sic) for a variety V over a number field is weak approximation (cf. approximation in algebraic groups See more WebDec 22, 2024 · Given a Hilbertian field $k$ and a finite set $\mathcal{S}$ of Krull valuations of $k$, we show that every finite split embedding problem $G \rightarrow {\rm{Gal}}(L ... tim greyhound bus