Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I
arXiv:1210.7894 · doi:10.2140/ant.2016.10.451
Abstract
The obstruction to the local-global principle for a hermitian lattice (L, H) can be quantified by computing the mass of (L, H). The mass formula expresses the mass of (L, H) as a product of local factors, called the local densities of (L, H). The local density formula is known except in the case of a ramified hermitian lattice of residue characteristic 2. Let F be a finite unramified field extension of Q_2. Ramified quadratic extensions E/F fall into two cases that we call Case 1 and Case 2. In this paper, we obtain the local density formula for a ramified hermitian lattice in Case 1, by constructing a smooth integral group scheme model for an appropriate unitary group. Consequently, this paper, combined with the paper of W. T. Gan and J.-K. Yu, allows the computation of the mass formula for a hermitian lattice (L, H) in Case 1.
70 pages. The previous version is divided into two papers (Case 1 and Case 2). The current version is for Case 1 and its final version (for Case 1) is to appear in Algebra & Number Theory
References in corpus (3)
Cited by in corpus (7)
- Universality of the cokernels of random -adic Hermitian matrices
- Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part II, Expanded version
- A reformulation of the Siegel series and intersection numbers
- Reflective obstructions of unitary modular varieties
- Relations among smooth integral models associated to quadratic, symplectic and hermitian lattices
- A uniform construction of smooth integral models and a recipe for computing local densities
- The Hirzebruch-Mumford covolume of some hermitian lattices