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Grundlagen

In: Kommutative Algebra und Algebraische Geometrie

Author

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  • Jürgen Böhm

Abstract

Zusammenfassung Die Begriffe Kategorie, Funktor und natürliche Transformation werden definiert, adjungierte Funktoren und das Yoneda-Lemma vorgestellt, direkte Summen und Produkte, direkter und inverser Limes, Faserprodukt und Fasersumme eingeführt. Es folgt ein Kurzabriss über abelsche Kategorien und Diagrammbeweise in diesen. Topologische Räume werden definiert, ebenso lokal-abgeschlossene und irreduzible Teilmengen sowie noethersche topologische Räume und der Dimensionsbegriff mit Ketten irreduzibler Teilmengen. Es folgt eine in sich abgeschlossene Einführung in Grundbegriffe der homologischen Algebra, injektive und projektive Auflösungen, Konstruktion derivierter Funktoren, lange exakte Kohomologiesequenz, Berechnung der Kohomologie mit azyklischen Objekten, universelle δ-Funktoren und schließlich Grundtatsachen über Spektralsequenzen mit Konstruktion der Grothendieck-Spektralsequenz über eine Cartan-Eilenberg-Auflösung.

Suggested Citation

  • Jürgen Böhm, 2019. "Grundlagen," Springer Books, in: Kommutative Algebra und Algebraische Geometrie, chapter 0, pages 1-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-59482-7_1
    DOI: 10.1007/978-3-662-59482-7_1
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