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Preprint Number 182

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182. Franck Benoist, Elisabeth Bouscaren, and Anand Pillay
Semiabelian varieties over separably closed fields, maximal divisible subgroups, and exact sequences

Submission date: 14 April 2009.


Given a separably closed field K of characteristic p > 0 and degree of imperfection finite (often 1) we study the #-functor which takes a semiabelian variety G over K to the maximal divisible subgroup 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 our results, where differential algebraic methods are more prominent.

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