Noncommutative resolutions using syzygies
  Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise, via suitable syzygies, to a noncommutative resolution. 
Hailong Dao, Osamu Iyama, Srikanth B. Iyengar, Ryo Takahashi, Michael   Wemyss and Yuji Yoshino
math.RT math.AC