The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Pekeris Room, Ziskind Building on Tuesday, January 10, 2012 11:00 - 13:00 Note the unusual day and location Lior Bary-Soroker TAU will speak on Hilbert's irreducibility theorem and Galois representations Abstract: Hilbert's irreducibility theorem asserts if f is a polynomial in two variables X,Y with integral coefficients that is irreducible and of degree at least 1 in Y, then there exists an irreducible specialization, i.e. a rational number a, such that f(a,Y) is irreducible. A field with irreducible specializations is called Hilbertian. The numerous applications of this theorem makes the question of under what conditions an extension of a Hilbertian field is again Hilbertian. It turns out the the most difficult part is separable algebraic extensions. Jarden conjectured that if K is Hilbertain, A abelian variety over K, and E/K is an extension of K that is contained in the field generated by all torsion points of A, then E is Hilbertian. In this talk I shall discuss a solution of the conjecture using Galois representations. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>