Extensions of valuation rings containing $\mathbf{Q}$ as limits of smooth algebras

Abstract

We give a necessary and sufficient condition for an extension of valuation rings containing $\mathbf{Q}$ to be a filtered direct limit of smooth algebras.

arXiv commentIn this form will appear in Bull. Math. Soc. Sci. Math. Roumanie, 65(113), (2022), No 2. arXiv admin note: text overlap with arXiv:1910.09123