An elementary and constructive proof of Grothendieck's generic freeness lemma

Ingo Blechschmidt

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Submission date: 31. Aug. 2018
Pages: 7
Bibtex
MSC-Numbers: 13C05
Keywords and phrases: generic freeness lemma
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Link to arXiv: See the arXiv entry of this preprint.

Abstract:
We present a new and direct proof of Grothendieck's generic freeness lemma in its general form. Unlike the previously published proofs, it does not proceed in a series of reduction steps and is fully constructive, not using the axiom of choice or even the law of excluded middle. It was found by unwinding the result of a general topos-theoretic technique.