On subgroups of semi-abelian varieties defined by difference equations
We study the induced structure on definable groups in existentially closed difference fields. If G is a definable subgroup of a semi-abelian variety, orthogonal to every definable field, we show that G is stable and stably embedded; every definable subset of Gn is a Boolean combination of cosets of...
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| 格式: | Journal article |
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American Mathematical Society
2016
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| 總結: | We study the induced structure on definable groups in existentially closed difference fields. If G is a definable subgroup of a semi-abelian variety, orthogonal to every definable field, we show that G is stable and stably embedded; every definable subset of Gn is a Boolean combination of cosets of definable subgroups of Gn, and Gn has at most countably many definable subgroups. This generalises to positive characteristic earlier results of the authors. |
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