Blow up dynamics for equivariant critical Schr\"odinger maps

For the Schr"odinger map problem from 2+1 dimensions into the 2-sphere we prove the existence of equivariant finite time blow up solutions that are close to a dynamically rescaled lowest energy harmonic map, the scaling parameter being given by $t^{-\nu }$ with $\nu >3\mathrm{/}2$.