  The holographic duality can be extended to include quantum theories with
broken coordinate invariance leading to the appearance of the gravitational
anomalies. On the gravity side one adds the gravitational Chern-Simons term to
the bulk action which gauge invariance is only up to the boundary terms. We
analyze in detail how the gravitational anomalies originate from the modified
Einstein equations in the bulk. As a side observation we find that the
gravitational Chern-Simons functional has interesting conformal properties. It
is invariant under conformal transformations. Moreover, its metric variation
produces conformal tensor which is a generalization of the Cotton tensor to
dimension $d+1=4k-1, k\in Z$. We calculate the modification of the holographic
stress-energy tensor that is due to the Chern-Simons term and use the bulk
Einstein equations to find its divergence and thus reproduce the gravitational
anomaly. Explicit calculation of the anomaly is carried out in dimensions $d=2$
and $d=6$. The result of the holographic calculation is compared with that of
the descent method and agreement is found. The gravitational Chern-Simons term
originates by Kaluza-Klein mechanism from a one-loop modification of M-theory
action. This modification is discussed in the context of the gravitational
anomaly in six-dimensional $(2,0)$ theory. The agreement with earlier
conjectured anomaly is found.
