  A persistence module with $m$ discrete parameters is a diagram of vector
spaces indexed by the poset $\mathbb{N}^m$. If we are only interested in the
large scale behavior of such a diagram, then we can consider two diagrams
equivalent if they agree outside of a ``negligeable'' region. In the
$2$-dimensional case, we classify the indecomposable diagrams up to finitely
supported diagrams. In higher dimension, we partially classify the
indecomposable diagrams up to suitably finite diagrams, and show that the full
classification problem is wild.
