Outline of lectures on Model Theory and

The general theme will be the use of model-theoretic methods in proofs of the Manin-Mumford conjecture and variants. If K is an algebraically closed field, G a commutative algebraic group over K and Γ an abstract subgroup of G(K), we will say that Γ is of Lang type, if for any n and subvariety X of G, X(K) ∩ Γ is a finite union of cosets of subgroups of Γ. The Manin-Mumford conjecture says that if the characteristic is 0 and G is a semiabelian variety, then the group Tor(G) of torsion points of G(K) is of Lang type. Hrushovski [7] gave a proof of the Manin-Mumford conjecture, using the model theory of difference fields [3]. Scanlon [13] proved “Manin-Mumford for Drinfeld modules” in positive characteristic (see below), also using the model theory of difference fields [4].