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Spektren, Garben, Schemata
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Das essential fhrt in die wesentlichen Konzepte der modernen algebraischen Geometrie ein. Dabei werden zunchst algebraische Grundbegriffe wiederholt. Die algebraische Struktur eines kommutativen Ringes spiegelt sich in der Menge seiner Primideale wider. Diese Menge kann mit einer topologischen Struktur versehen werden; dies ist der Begriff des Spektrums, der also algebraische in topologische Daten bersetzt. Mithilfe des Begriffs der Garbe kann man aus dieser topologischen die algebraische Struktur zurckgewinnen. Dieses reichhaltige Wechselspiel wird im Begriff des Schemas erfasst. Dadurch kann man die grundlegenden Objekte der algebraischen Geometrie, Nullstellengebilde von Polynomen, algebraisch untersuchen und umgekehrt geometrische Methoden auf arithmetische Fragen anwenden.
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