Quantum Consistency of the Superstring in AdS_5 x S^5 Background
  Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS_5 x S^5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level. 
Nathan Berkovits (IFT-UNESP, Sao Paulo)