Is there a Noether normalisation lemma for finitely generated (flat) algebras over $\mathbf{Z}$ (or more generally principal ideal domains)? It seems one can tensorise with the quotient field and then apply the usual Noether normalisation lemma. I couldn't find this in the literature, so I suspect it is wrong.
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$\begingroup$ Related? mathoverflow.net/questions/42276/… $\endgroup$– AsvinCommented Oct 20, 2017 at 17:14
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1$\begingroup$ Isn't this the same question? math.stackexchange.com/questions/213336/… $\endgroup$– AsvinCommented Oct 20, 2017 at 17:16
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$\begingroup$ @Asvin: Thanks! Can one omit the localisation in the case of a PID and a flat algebra? $\endgroup$– user19475Commented Oct 20, 2017 at 17:33
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$\begingroup$ I haven't actually gone through the links myself. I just remembered seeing similar questions before. Maybe you will find the formulation here more useful? mathoverflow.net/a/60716/58001 $\endgroup$– AsvinCommented Oct 20, 2017 at 17:47
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1$\begingroup$ Another reference in the literature is Proposition 2.1 of Jouanolou, "Théorèmes de Bertini et applications." $\endgroup$– Aaron LandesmanCommented Oct 21, 2017 at 5:40
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1 Answer
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you can consult the paper Corrigendum to “Noether Normalization theorem and dynamical Gröbner bases over Bezout domains of Krull dimension 1” [J. Algebra 492 (15) (2017) 52-56] by Maroua Gamanda and Ihsen Yengui.
The link is https://www.sciencedirect.com/science/article/pii/S002186931930314X
