  In this paper, we explain a simple and uniform construction of a smooth
integral model associated to a quadratic, (anti)-hermitian, and
(anti)-quaternionic hermitian lattice defined over an arbitrary local field. As
one major application, we explain a recipe for computing local densities case
by case, which is an essential factor in the classification of forms as above
over the ring of integers of a number field, by introducing one conjecture
about the number of rational points of the special fiber of a smooth integral
model.
