The Schinzel hypothesis is a famous conjectural statement about
primes in value sets of polynomials, which generalizes the Dirichlet theorem
about primes in an arithmetic progression. We consider the situation that
the ring of integers is replaced by a polynomial ring and prove the Schinzel
hypothesis for a wide class of them: polynomials in at least one variable over
the integers, polynomials in several variables over an arbitrary field, etc.
We achieve this goal by developing a version over rings of the Hilbert
specialization property. (Joint work with Arnaud Bodin and Salah Najib).
Galois Seminar
Friday, April 26, 2019 - 3:15pm
Pierre Dèbes
Université de Lille