Deformations of Lie groupoids can be studied by means of the intrinsic

cohomology that controls them. This approach is related both to the

study of deformations of Lie group actions by Palais, and to the

linearization theorem for proper Lie groupoids. We obtain a vanishing

result for the deformation cohomology of proper Lie groupoids and a

rigidity result for compact Lie groupoids.

The aim of this talk is to present this intrinsic deformation

cohomology and the two mentioned results, giving an idea of their

proofs.

The talk is based on joint work with Marius Crainic and Ivan Struchiner.