  We analyse scale anomalies in Lifshitz field theories, formulated as the
relative cohomology of the scaling operator with respect to foliation
preserving diffeomorphisms. We construct a detailed framework that enables us
to calculate the anomalies for any number of spatial dimensions, and for any
value of the dynamical exponent. We derive selection rules, and establish the
anomaly structure in diverse universal sectors. We present the complete
cohomologies for various examples in one, two and three space dimensions for
several values of the dynamical exponent. Our calculations indicate that all
the Lifshitz scale anomalies are trivial descents, called B-type in the
terminology of conformal anomalies. However, not all the trivial descents are
cohomologically non-trivial. We compare the conformal anomalies to Lifshitz
scale anomalies with a dynamical exponent equal to one.
