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. Also desumoylates RPA1, thus preventing recruitment of RAD51 to the DNA damage foci to initiate DNA repair through homologous recombination. {ECO:0000269|PubMed:16912044, ECO:0000269|PubMed:17000875, ECO:0000269|PubMed:18799455, ECO:0000269|PubMed:20212317, ECO:0000269|PubMed:20705237, ECO:0000269|PubMed:21148299}. This is the function of ENSG00000112701 (SENP6, SUMO specific peptidase 6).