Publikation: On varieties of Hilbert type
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2013
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Zusammenfassung
A variety X over a field K is of Hilbert type if the set of rational points X(K) is not thin. We prove that if f: X\to S is a dominant morphism of K-varieties and both S and all fibers f^{-1}(s), s in S(K), are of Hilbert type, then so is X. We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Th'el`ene and Sansuc on algebraic groups.
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Fachgebiet (DDC)
510 Mathematik
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Algebraic Geometry (math.AG), Number Theory (math.NT)
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BARY-SOROKER, Lior, Arno FEHM, Sebastian PETERSEN, 2013. On varieties of Hilbert typeBibTex
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<dcterms:abstract xml:lang="eng">A variety X over a field K is of Hilbert type if the set of rational points X(K) is not thin. We prove that if f: X\to S is a dominant morphism of K-varieties and both S and all fibers f^{-1}(s), s in S(K), are of Hilbert type, then so is X. We apply this to answer a question of Serre on products of varieties and to generalize a result of Colliot-Th'el`ene and Sansuc on algebraic groups.</dcterms:abstract>
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