François Charles Explores Bertini Theorems in Arithmetic Geometry 📚

Abstract: The classical Bertini irreducibility theorem states that if X is an irreducible projective variety of dimension at least 2 over an infinite field, then X has an irreducible hyperplane section. The proof does not apply in arithmetic situations, where one wants to work over the integers or a finite fields. I will discuss how to amend the theorem in these cases (joint with Bjorn Poonen over finite fields).

Recording during the thematic meeting : "Rational Points and Algebraic Geometry " the September 29, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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