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Vanishing Cycle
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Geliefert zwischen Mo., 06.04.2026 und Di., 07.04.2026
Details
High Quality Content by WIKIPEDIA articles! In mathematics, vanishing cycles are studied in singularity theory and other part of algebraic geometry. They are those homology cycles of a smooth fiber in a family which vanish in the singular fiber.A classical result is the Picard-Lefschetz formula, detailing how the monodromy round the singular fiber acts on the vanishing cycles, by a shear mapping. The classical, geometric theory of Solomon Lefschetz was recast in purely algebraic terms, in SGA7. This was for the requirements of its application in the context of l-adic cohomology; and eventual application to the Weil conjectures. There the definition uses derived categories, and looks very different. It involves a functor, the nearby cycle functor, with a definition by means of the higher direct image and pullbacks. The vanishing cycle functor then sits in a distinguished triangle with the nearby cycle functor and a more elementary functor. This formulation has been of continuing influence, in particular in D-module theory.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131117701
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Titel Vanishing Cycle
- Format Fachbuch
- EAN 9786131117701
- Genre Musik
- Anzahl Seiten 80
- Herausgeber Betascript Publishing
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