= Integral lattice in a p-adic vector space
{title2=$\Lambda\otimes_{\mathbb Z_p}\mathbb Q_p=V$}
= p-adic lattice
{synonym}
An integral lattice in a finite-dimensional $\mathbb Q_p$-vector space is a free $\mathbb Z_p$-submodule of full rank. Any two such lattices are commensurable: their intersection has finite index in each, because a sufficiently large power of $p$ multiplies either into the other. A finite group acting on the space admits invariant lattices by taking a sum of translates. This allows <Herbrand quotient> comparisons via finite quotient modules.
Back to article page
