Shadows in Linear Lattices

this paper we investigate the Kruskal-Katona type problem for linear lattices. First (section 2) we show that there is a dual problem to the minimization problem, namely the maximization of the cardinality of the "reverse shadow" which will be defined later. We prove that the minimization problem and the maximization problem are equisolvable. In section 3 we relax the problem by asking for which subset S of (GF (q)

The p-adic Uniformization of Shimura Curves

Introduction Let us denote by the complex manifold C n R by X. The group Gl 2 (R) acts via linear fractional transformations from the left on X. We consider arithmetically defined subgroups \Gamma ae Gl 2 (R), which are obtained as follows. Let D be a quaternion division algebra over a totally real number field F . We assume that there is a single archimedean place ff : F ! R such that D splits in ff: D\Omega F;ff R ¸ = M 2 (R) At all other archimedian places D is a division algebra. Let G be the multiplicative group of D considered as an algebraic group over Q . We have a natural decom