Abstract
Let M be any order of a quaternion algebra Q over a local field F. The group Mx of units and the central Picard group Picent (M) of M are investigated. The group index (Lx:Mx) and, if F is of characteristic ≠2, also the norms of all primitive ideals of M and the order of Picent (M) are determined explicitly, where L denotes any maximal order of Q containing M. Applications of these results to local densities of ternary quadratic forms and to class numbers and type numbers of global quaternion orders are indicated.
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Körner, O. Über die zentrale Picard-Gruppe und die Einheiten lokaler Quaternionenordnungen. Manuscripta Math 52, 203–225 (1985). https://doi.org/10.1007/BF01171492
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DOI: https://doi.org/10.1007/BF01171492