Superrigidity Theorems in Positive Characteristic,

We generalize the superrigidity theorem of G. A. Margulis (1991, “Discrete Subgroups of Semisimple Lie Groups,” VII.5.19, Springer-Verlag, New York/Berlin) to the case of the more general non-reductive target group F. We also provide a proof of the cocycle superrigidity theorem in the case of algebraic groups defined over a local field of positive characteristic and the generalization of this proof to the case of the more general target group analogous to our generalization of the superrigidity theorem.