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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 5, Pages 3–18 (Mi izv38)  

This article is cited in 3 scientific papers (total 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.

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

Bibliographic databases:

MSC: 14E30, 12F05, 13G05
Received: 09.11.1994

Citation: V. E. Voskresenskii, T. V. Fomina, “Integral structures in algebraic tori”, Izv. RAN. Ser. Mat., 59:5 (1995), 3–18; Izv. Math., 59:5 (1995), 881–897

Citation in format AMSBIB
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\by V.~E.~Voskresenskii, T.~V.~Fomina
\paper Integral structures in algebraic tori
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 5
\pages 3--18
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1360631}
\zmath{https://zbmath.org/?q=an:0899.20025}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 5
\pages 881--897
\crossref{https://doi.org/10.1070/IM1995v059n05ABEH000038}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UH54100001}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kunyavskii B., Sansuc J., “An Inverse Problem for Reduction of Commutative Algebraic Groups”, Comptes Rendus Acad. Sci. Ser. I-Math., 324:3 (1997), 307–312  crossref  mathscinet  zmath  adsnasa  isi
    2. Kunyavskii R., Sansuc J., “Reduction of Commutative Algebraic Groups”, J. Math. Soc. Jpn., 53:2 (2001), 457–483  crossref  mathscinet  zmath  isi
    3. S.Y.u Popov, Valentin Voskresenskii, “GALOIS LATTICES AND REDUCTIONS OF ALGEBRAIC TORI”, Communications in Algebra, 29:9 (2001), 3711  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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