Protease that deconjugates SUMO1; SUMO2 and SUMO3 from targeted proteins. Processes preferentially poly-SUMO2 and poly- SUMO3 chains; but does not efficiently process SUMO1; SUMO2 and SUMO3 precursors. Deconjugates SUMO1 from RXRA; leading to transcriptional activation. Involved in chromosome alignment and spindle assembly; by regulating the kinetochore CENPH-CENPI-CENPK complex. Desumoylates PML and CENPI; protecting them from degradation by the ubiquitin ligase RNF4; which targets polysumoylated proteins for proteasomal degradation. Desumoylates also RPA1; thus preventing recruitment of RAD51 to the DNA damage foci to initiate DNA repair through homologous recombination.