k-derivations and finite morphisms
نویسنده
چکیده
Let G be an affine algebraic group over an algebraically closed field k of characteristic zero. In this paper, we consider finite G-equivariant morphisms F : X → Y of irreducible affine varieties. First we determine under which conditions on Y the induced map FG : X//G → Y//G of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on k-algebras A ⊂ B such that B is integral over A. Second we construct explicitly two examples of finite G-equivariant maps F . In the first one, FG is quasifinite but not finite. In the second one, FG is not even quasifinite.
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