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ЖУРНАЛЫ // Известия Российской академии наук. Серия математическая // Архив

Изв. РАН. Сер. матем., 1996, том 60, выпуск 2, страницы 149–158 (Mi im74)

Эта публикация цитируется в 3 статьях

Hodge groups of abelian varieties with purely multiplicative reduction

A. Silverberga, Yu. G. Zarhinb

a Ohio State University
b Institute of Mathematical Problems of Biology, Russian Academy of Sciences

Аннотация: The main result of the paper is that if $A$ is an abelian variety over a subfield $F$ of $\mathbf C$, and $A$ has purely multiplicative reduction at a discrete valuation of $F$, then the Hodge group of $A$ is semisimple. Further, we give necessary and sufficient conditions for the Hodge group to be semisimple. We obtain bounds on certain torsion subgroups for abelian varieties which do not have purely multiplicative reduction at a given discrete valuation, and therefore obtain bounds on torsion for abelian varieties, defined over number fields, whose Hodge groups are not semisimple.
Bibliography: 26 titles.

УДК: 513.6

MSC: Primary 14K15; Secondary 11G10

Поступило в редакцию: 13.06.1995

Язык публикации: английский

DOI: 10.4213/im74


 Англоязычная версия: Izvestiya: Mathematics, 1996, 60:2, 379–389

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