  This is a short review of the papers arXiv:1109.2904 and arXiv:1110.4639.
After a reminder about local and global gravitational anomalies, we sketch the
derivation of the global gravitational anomaly of the self-dual field theory
(also known as chiral p-form). We then show that "cohomological" type IIB
supergravity is free of global gravitational anomalies on all ten-dimensional
spin manifolds
