Semi-Continuity for Derived Categories
  We prove that the number of parameters defining a complex of projective modules over a finite dimensional algebra is upper semi-continuous in families of algebras. Supposing that every algebra is either derived tame or derived wild, we get that a degeneration of a derived wild algebra is derived wild too. We also explain why the so-called counter-example of Bruestle is in fact not a counter-example. 
Yuriy A. Drozd (Kyiv Taras Shevchenko University)