A uniform construction of smooth integral models and a recipe for computing local densities
arXiv:1412.6218 · doi:10.1093/imrn/rnw340
Abstract
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.
18 pages
References in corpus (3)
- Group schemes and local densities of quadratic lattices in residue characteristic 2
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part II, Expanded version