Pure transcendental, immediate valuation ring extensions as limits of smooth algebras
Abstract
We show that a pure transcendental, immediate extension of valuation rings $V\subset V'$ containing a field is a filtered union of smooth $V$-subalgebras of $V'$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- arXiv:
- arXiv:2206.00472
- Bibcode:
- 2022arXiv220600472P
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry
- E-Print:
- Lemma 23 was removed being not necessary and more details are given in the proof of Corollary 20