Weak Formal Schemes
نویسندگان
چکیده
منابع مشابه
Program Schemes, Recursion Schemes, and Formal Languages
This paper presents general methods for studying the problems of translatability between classes of schemes and equivalence of schemes in a given class. There are four methods: applying the theory of formal languages, programming, measuring the complexity of a computation, and "cutting and pasting." These methods are used to answer several questions of translatability and equivalence for classe...
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One feature which clearly distinguishes the theory of schemes from the older theory of varieties is the possibility of having nilpotent elements in the structure sheaf of a scheme. In particular, if Y is a closed subvariety of a variety X, defined by a sheaf of ideals I , then for any n ≥ 1 we can consider the closed subscheme Yn defined by the nth power I n of the sheaf of ideals I . For n ≥ 2...
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Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in nonNoetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a proringed space and study its basic properties. We also find several examples of non-adic formal schemes.
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We think about what the subscheme of the formal scheme is. Differently form the ordinary scheme, the formal scheme has different notions of “subscheme”. We lay a foundation for these notions and compare them. We also relate them to singularities of foliations.
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Let (X,OX) be a noetherian separated formal scheme and consider D(Aqct(X)), its associated derived category of quasi-coherent torsion sheaves. We show that there is a bijection between the set of rigid localizations in D(Aqct(X)) and subsets in X. For a stable for specialization subset Z ⊂ X, the associated acyclization is RΓZ . If Z ⊂ X is generically stable, we provide a description of the as...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1972
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000014641