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Annali di Matematica Pura ed Applicata

, Volume 105, Issue 1, pp 191–204 | Cite as

Ideali di definizione e morfismi di schemi henseliani

  • Fulvio Mora
Article
  • 23 Downloads

Summary

Given a pair (A,M), where A is a complete ring with respect toM-adic topology, we can define theformal spectrum of A: this is the basic concept of the theory offormal schemes (see[4], I, § 10). In a similar way, given a Hensel pair (A,M), we can develope a theory ofHenselian schemes. In this work we study some properties of Henselian schemes, like the existence ofdefinition ideals (def.2.3) which are useful to have a « good definition » ofmorphisms (def.3.10) and, in particular, ofadic morphisms (def.3.11). At the end, after some remarks about henselian product of pairs, we prove the existence and uniqueness of product in the category of Henselian schemes (prop.4.7) and we apply the above results to adic morphisms (prop.4.9).

Bibliografia

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    N. Bourbaki,Algebre Commutative, ch. I et II, Hermann, Paris, 1961.Google Scholar
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    S. Greco,Henselization of a ring with respect to an ideal, Trans. A.M.S.,144 (1969), pp. 43–65.CrossRefzbMATHMathSciNetGoogle Scholar
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    S. Greco,Sulla nozione di preschema henseliano, Rend. Accademia Naz. dei Lincei,50 (1971), pp. 78–81.MathSciNetGoogle Scholar
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    A. Grothendieck,Eléments de Géométrie Algébrique, Springer-Verlag, Berlin, 1971.Google Scholar
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    H. Kurke,Grundlagen der Theorie der Henselschen Ringe und Schemata und ihrer Anwendungen, Tesi, Humboldt Universitat zu Berlin, 1969.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Fulvio Mora
    • 1
  1. 1.Genova

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