Algebra & Number Theory
- Algebra Number Theory
- Volume 10, Number 3 (2016), 451-532.
Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I
The obstruction to the local-global principle for a hermitian lattice can be quantified by computing the mass of . The mass formula expresses the mass of as a product of local factors, called the local densities of . The local density formula is known except in the case of a ramified hermitian lattice of residue characteristic 2.
Let be a finite unramified field extension of . Ramified quadratic extensions 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 (Duke Math. J. 105 (2000), 497–524), allows the computation of the mass formula for a hermitian lattice in Case 1.
Algebra Number Theory, Volume 10, Number 3 (2016), 451-532.
Received: 30 August 2013
Revised: 15 September 2015
Accepted: 25 October 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11E41: Class numbers of quadratic and Hermitian forms
Secondary: 11E95: $p$-adic theory 14L15: Group schemes 20G25: Linear algebraic groups over local fields and their integers 11E39: Bilinear and Hermitian forms 11E57: Classical groups [See also 14Lxx, 20Gxx]
Cho, Sungmun. Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I. Algebra Number Theory 10 (2016), no. 3, 451--532. doi:10.2140/ant.2016.10.451. https://projecteuclid.org/euclid.ant/1510842494