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On the Hilbert Irreducibility Theorem

By U. Zannier


We discuss the Hilbert Irreducibility Theorem, presenting briefly a new approach which leads to novel conclusions, especially in the context of algebraic groups. After a short survey of the issues and of the known theory, we shall illustrate the main principles and mention some new results; in particular, we shall state a toric analogue of Bertini’s Theorem and a lifting theorem for rational points on a cover of a power of an elliptic curve

Year: 2009
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