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Galois Seminar

Friday, April 26, 2019 - 3:15pm

Pierre Dèbes

Université de Lille


University of Pennsylvania

DRL 4N30

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).