On the $\partial\overline{\partial}$-Lemma and Bott-Chern cohomology
  On a compact complex manifold $X$, we prove a Fr\"olicher-type inequality for Bott-Chern cohomology and we show that the equality holds if and only if $X$ satisfies the $\partial\overline{\partial}$-Lemma. 
Daniele Angella, Adriano Tomassini
math.DG math.CV