  Symmetry indicators have proven to be extremely helpful in identifying
topologically non-trivial crystalline insulators using symmetry-group
representations of their Bloch states. An extension of this approach to
superconducting systems requires defining an appropriate atomic limit for
Bogoliubov-de-Gennes Hamiltonians. Here, we introduce such a notion of atomic
limit and derive a $\mathbb{Z}_{2^d}$-valued symmetry indicator for
inversion-symmetric superconductors of $d$ dimensions. This indicator allows
for a refined topological classification including higher-order phases for
systems in the superconducting symmetry classes D and DIII. We further
elucidate the bulk-boundary correspondence of these phases using Dirac surface
theories. Requiring only the normal-state band structure and the
superconducting order-parameter symmetry as an input, this indicator is well
suited for a search of topological superconductors using first-principles
calculations.
