Temat: algebraic varieties - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On the intersection multiplicity of images under an etale morphism
Autorzy:: Nowak, Krzysztof
Powiązania:: https://bibliotekanauki.pl/articles/966012.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: intersection multiplicity
multiplicity of ideals in a semilocal ring
etale morphisms
unramified morphisms
algebraic varieties
Opis:: We present a formula for the intersection multiplicity of the images of two subvarieties under an etale morphism between smooth varieties over a field k. It is a generalization of Fulton's Example 8.2.5 from [3], where a strong additional assumption has been imposed. In a special case where the base field k is algebraically closed and a proper component of the intersection is a closed point, intersection multiplicity is an invariant of etale morphisms. This corresponds with analytic geometry where intersection multiplicity is an invariant of local biholomorphisms.
Źródło:: Colloquium Mathematicum; 1998, 75, 2; 167-174
0010-1354
Pojawia się w:: Colloquium Mathematicum
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts
Autorzy:: Sayed Ahmed, Tarek
Powiązania:: https://bibliotekanauki.pl/articles/43189294.pdf
Data publikacji:: 2024
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: algebraic logic
systems of varieties
ultraproducts
non-finite axiomaitizability
Opis:: We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite. Let \(\bf Ord\) denote the class of all ordinals. Let \(\langle \mathbf{K}_{\alpha}: \alpha\in \bf Ord\rangle\) be a system of varieties definable by a schema. Given any ordinal \(\alpha\), we define an operator \(\mathsf{Nr}_{\alpha}\) that acts on \(\mathbf{K}_{\beta}\) for any \(\beta>\alpha\) giving an algebra in \(\mathbf{K}_{\alpha}\), as an abstraction of taking \(\alpha\)-neat reducts for cylindric algebras. We show that for any positive \(k\), and any infinite ordinal \(\alpha\) that \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k+1}\) cannot be axiomatized by a finite schema over \(\mathbf{S}\mathsf{Nr}_{\alpha}\mathbf{K}_{\alpha+k}\) given that the result is valid for all finite dimensions greater than some fixed finite ordinal. We apply our results to cylindric algebras and Halmos quasipolyadic algebras with equality. As an application to our algebraic result we obtain a strong incompleteness theorem (in the sense that validitities are not captured by finitary Hilbert style axiomatizations) for an algebraizable extension of \(L_{\omega,\omega}\).
Źródło:: Bulletin of the Section of Logic; 2024, 53, 2; 145-154
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

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