Finiteness results for Hilbert's irreducibility theorem
نویسندگان
چکیده
منابع مشابه
Finiteness Results for Hilbert’s Irreducibility Theorem
Let k be a number field, Ok its ring of integers, and f(t,X) ∈ k(t)[X] be an irreducible polynomial. Hilbert’s irreducibility theorem gives infinitely many integral specializations t 7→ t̄ ∈ Ok such that f(t̄, X) is still irreducible. In this paper we study the set Redf (Ok) of those t̄ ∈ Ok with f(t̄, X) reducible. We show that Redf (Ok) is a finite set under rather weak assumptions. In particular...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2002
ISSN: 0373-0956
DOI: 10.5802/aif.1907