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>