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Zbl 0803.03023
Messmer, Margit
Groups and fields interpretable in separably closed fields. (English)
[J] Trans. Am. Math. Soc. 344, No.1, 361-377 (1994). ISSN 0002-9947; ISSN 1088-6850/e

Summary: We prove that any infinite group interpretable in a separably closed field $F$ of finite Ershov-invariant is definably isomorphic to an $F$- algebraic group. Using this result we show that any infinite field $K$ interpretable in a separably closed field $F$ is itself separably closed; in particular, in the finite invariant case $K$ is definably isomorphic to a finite extension of $F$.

MSC 2000:: *03C60 Model-theoretic algebra
12L12 Model theory for fields

Keywords: infinite group; separably closed field; finite Ershov-invariant; $F$- algebraic group; infinite field

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