1. On Hilbert's Irreducibility Theorem
- Author
-
Michael D. Fried
- Subjects
Algebra ,Algebra and Number Theory ,Hilbert's irreducibility theorem ,Finite field ,Picard–Lindelöf theorem ,Fundamental theorem ,Absolutely irreducible ,Diophantine geometry ,Diophantine equation ,Irreducibility ,Mathematics::Representation Theory ,Mathematics - Abstract
A method for obtaining very precise results along the lines of the Hilbert Irreducibility Theorem is described and then applied to a special case. In addition, the relationship of the irreducibility theorem to other tools of diophantine analysis is investigated. In particular, we give a proof of the irreducibility theorem that uses only Noether's lemma and the fact that an absolutely irreducible curve has a rational point over a finite field of large order.
- Published
- 1974