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).
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Bibliografia
N. Bourbaki,Algebre Commutative, ch. I et II, Hermann, Paris, 1961.
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H. Kurke,Grundlagen der Theorie der Henselschen Ringe und Schemata und ihrer Anwendungen, Tesi, Humboldt Universitat zu Berlin, 1969.
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Entrata in Redazione il 26 novembre 1973.
Durante la preparazione del presente lavoro, l’A. ha fruito di una borsa di studio del C.N.R.
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Mora, F. Ideali di definizione e morfismi di schemi henseliani. Annali di Matematica 105, 191–204 (1975). https://doi.org/10.1007/BF02414929
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DOI: https://doi.org/10.1007/BF02414929