Title: AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions,
Abstract: We explore all warped $AdS_4\times_w M^{D-4}$ backgrounds with the most
general allowed fluxes that preserve more than 16 supersymmetries in $D=10$-
and $11$-dimensional supergravities. After imposing the assumption that either
the internal space $M^{D-4}$ is compact without boundary or the isometry
algebra of the background decomposes into that of AdS$_4$ and that of
$M^{D-4}$, we find that there are no such backgrounds in IIB supergravity.
Similarly in IIA supergravity, there is a unique such background with 24
supersymmetries locally isometric to $AdS_4\times \mathbb{CP}^3$, and in $D=11$
supergravity all such backgrounds are locally isometric to the maximally
supersymmetric $AdS_4\times S^7$ solution.