Transfer and local density for Hermitian lattices

Abstract

In this paper we study the integral structure of lattices over finite extensions of \(\mathbb {Z}_p\) which arise from restriction or transfer from a lattice over a finite extension. We describe explicitly the structure of the resulting lattices. Special attention is given to the case of lattices whose quadratic forms arise from Hermitian forms. Then, in the case of Hermitian lattices where the final lattice is over \(\mathbb {Z}_p\) we focus on the problem of computing the local densities.