This article is cited in 3 papers

Integral structures in algebraic tori

V. E. Voskresenskii, T. V. Fomina

Samara State University

Abstract: The main result is the construction of a minimal integral model of an algebraic torus defined over a complete non-Archimedean extension of an algebraic number field. The structure of such models is studied. The main problem is the study of the model in the case of a ramified splitting field. Reductions of these models with respect to a simple module are described. Minimal models of tori over the ring of algebraic integers are constructed. The local volumes and class numbers of some models are calculated.

MSC: 14E30, 12F05, 13G05

Received: 09.11.1994

 English version: Izvestiya: Mathematics, 1995, 59:5, 881–897

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