  Ramification for commutative ring spectra can be detected by relative
topological Hochschild homology and by topological Andr\'e-Quillen homology. In
the classical algebraic context it is important to distinguish between tame and
wild ramification. Noether's theorem characterizes tame ramification in terms
of a normal basis and tame ramification can also be detected via the
surjectivity of the trace map. We transfer the latter fact to ring spectra and
use the Tate cohomology spectrum to detect wild ramification in the context of
commutative ring spectra. We study ramification in examples in the context of
topological K-theory and topological modular forms.
