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Thin Set (Serre)
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Geliefert zwischen Mi., 26.11.2025 und Do., 27.11.2025
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High Quality Content by WIKIPEDIA articles! In mathematics, a thin set in the sense of Serre, named after Jean-Pierre Serre, is a certain kind of subset constructed in algebraic geometry over a given field K, by allowed operations that are in a definite sense 'unlikely'. The two fundamental ones are: solving a polynomial equation that may or may not be the case; solving within K a polynomial that does not always factorise. One is also allowed to take finite unions. More precisely, let V be an algebraic variety over K (assumptions here are: V is an irreducible set, a quasi-projective variety, and K has characteristic zero). A type I thin set is a subset of V(K) that is not Zariski-dense. That means it lies in an algebraic set that is a finite union of algebraic varieties of dimension lower than d, the dimension of V. A type II thin set is an image of an algebraic morphism (essentially a polynomial mapping) , applied to the K-points of some other d-dimensional algebraic variety V , that maps essentially onto V as a ramified covering with degree e 1.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131140631
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131140631
- Titel Thin Set (Serre)
- Herausgeber Betascript Publishing
- Anzahl Seiten 72
- Genre Mathematik
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