Hochster's small MCM conjecture for three-dimensional weakly F-split   rings
  We prove Hochster's small MCM conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We conjecture that any complete ring is weakly F-split. 
Hans Schoutens
math.AC