Hilbert’s Irreducibility Theorem shows that irreducibility over the field of rationals is ‘often’ preserved when one specializes a variable in some irreducible polynomial in several variables. I will present a version ‘over the ring’ for which the specialized polynomial remains irreducible over the ring of integers. The result also relates to the Schinzel Hypothesis about primes in value sets of polynomials: I will discuss a weaker ‘relative’ version for the integers and the full version for polynomials. The results extend to other base rings than the ring of integers; the general context is that of rings with a product formula.
Joint work with A. Bodin, J. Koenig and S. Najib.
This video was produced by Tel Aviv University as part of its algebra seminar.
