Groups and fields interpretable in separably closed fields

Messmer, Margit

doi:10.1090/S0002-9947-1994-1231337-6

Groups and fields interpretable in separably closed fields
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Trans. Amer. Math. Soc. 344 (1994), 361-377 Request permission

Abstract:

We prove that any infinite group interpretable in a separably closed field F of finite Eršov-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.

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Definable groups in characteristic

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