Mathematische Zeitschrift

, Volume 236, Issue 1, pp 201–214

Completions of local morphisms and valuations


  • Reinhold Hübl
    • NWF I – Mathematik, Universität Regensburg, D-93040 Regensburg, Germany (e-mail:
Original article

DOI: 10.1007/PL00004824

Cite this article as:
Hübl, R. Math Z (2001) 236: 201. doi:10.1007/PL00004824


In this note we study injective local morphisms \(\varphi: (R,{\mathfrak m})\rightarrow (S,{\mathfrak n})\) of local excellent domains. In particular we are interested in the problem when the \({\mathfrak n}\)–adic topology onS restricts to a topology on R that is linearly equivalent to the \({\mathfrak m}\)–adic topology. Using a valuative criterion, we prove this in case R is analytically irreducible and \(S/R\) is essentially of finite type, and we recover and extend a weak version of Gabrielov's rank condition.

Mathematics Subject Classification (1991):13A18, 14F10, 13B22
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© Springer-Verlag Berlin Heidelberg 2000