On Σ-hilbertian Fields
نویسندگان
چکیده
A field K is 0-Hilbertian if K 6= ⋃ni=1 φi(K) for any collection of rational functions φi of degree at least 2, i = 1, . . . ,m. Corvaja and Zannier [CoZ] give an elementary construction for a 0-Hilbertian field that isn’t Hilbertian. There is an obvious generalization of the notion of 0-Hilbertian to g-Hilbertian. Guralnick-Thompson and Liebeck-Saxl have given a partial classification of monodromy groups of genus g covers of the projective line over C. We use this to construct, for each nonnegative integer g, a PAC field K of characteristic 0 which is g-Hilbertian but not Hilbertian.
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تاریخ انتشار 1997