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We prove upper bounds on angular momentum and centre of mass in terms of theHamiltonian mass and cosmological constant for non-singular asymptoticallyanti-de Sitter initial data sets satisfying the dominant energy condition. Wework in all space-dimensions larger than or equal to three, and allow a largeclass of asymptotic backgrounds, with spherical and non-spherical conformalinfinities; in the latter case, a spin-structure compatibility condition isimposed. We give a large class of non-trivial examples saturating theinequality. We analyse exhaustively the borderline case in space-time dimensionfour: for spherical cross-sections of Scri, equality together with completenessoccurs only in anti-de Sitter space-time. On the other hand, in the toroidalcase, regular non-trivial initial data sets saturating the bound exist.Comment: improvements in the presentation; some statements correcte

Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times