Rigidity of the measurable structure for algebraic actions of higher   rank abelian groups
  We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries. 
Boris Kalinin (University of Michigan), Ralf Spatzier (University of   Michigan)