Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences

Details Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences

2009-04-14

arxiv.org/abs/0904.2083v1

Mathematics

Logic

41 pages

Scientific paper

Given a separably closed field K of positive characteristic and finite degree of imperfection we study the # functor which takes a semiabelian variety G over K to the maximal divisible subgroup #G of G(K). We show that the # functor need not preserve exact sequences. We relate preservation of exactness to issues of descent as well as to model theoretic properties of #G, and give an example where #G does not have "relative Morley rank". We also mention characteristic 0 versions of these results.

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