Riassunto
Il punto di partenza di questo lavoro è l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); ciò permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprietà. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine.
Summary
The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.
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Fontana, M., Mazzola, G. Arithmétique fonctorielle des topologies de Grothendieck. Ann. Univ. Ferrara 22, 49–94 (1976). https://doi.org/10.1007/BF02825077
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DOI: https://doi.org/10.1007/BF02825077