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Algebraische Funktionen einer Variablen

In: Algebra II

Author

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  • B. L. van der Waerden

Abstract

Zusammenfassung Die klassische Theorie der algebraischen Funktionen über dem Körper der komplexen Zahlen gipfelt im Satz von Riemann-Roch. Für diesen Satz gibt es funktionentheoretische, geometrische und algebraische Beweise. Eine schöne Darstellung der funktionentheoretischen Beweismethode mit Benutzung geometrischer Gedanken findet man bei C. Jobdan: Cours d’Analyse II, Chap. VIII. Unter den geometrischen Beweismethoden ist besonders die Metodo rapido von Severi hervorzuheben1. Der rein algebraische Beweis von Dedekind und Webee [J. reine u. angew. Math. 92 (1882)] wurde von Emmy Noetheb vereinfacht und auf vollkommene Konstantenkörper verallgemeinert. Für beliebige Konstantenkörper hat zuerst F. K. Schmidt den Riemann-Rochschen Satz bewiesen [Math. Z. 41 (1936); dort weitere Literatur]. Einen noch einfacheren Beweis gab AndbÉ Weil im J. reine u. angew. Math. 179 (1938); wir folgen hier seiner Methode.

Suggested Citation

  • B. L. van der Waerden, 1993. "Algebraische Funktionen einer Variablen," Springer Books, in: Algebra II, edition 0, chapter 0, pages 234-265, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-58038-3_8
    DOI: 10.1007/978-3-642-58038-3_8
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