Degree Bounds on Homology and a Conjecture of Derksen
  Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case. We provide counterexamples to this conjecture, but also prove a slightly weakened version.   We also prove some general results that give degree bounds on the homology of complexes and of Tor groups. 
Marc Chardin and Peter Symonds
math.AC