Global existence and uniqueness of Schr\"{o}dinger maps in dimensions   $d\geq 4$
  In dimensions $d\geq 4$, we prove that the Schr\"{o}dinger map initial-value problem admits global (in time) solutions for smooth data with small norm in the critical Sobolev space. 
I. Bejenaru, A. D. Ionescu, C. E. Kenig