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Field Theory for Function Fields of Plane Quartic Curves

✍ Scribed by Kei Miura; Hisao Yoshihara

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 113 KB
Volume: 226
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.8173

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✦ Synopsis

Let C be a smooth plane quartic curve over a field k and k C be a rational function field of C. We develop a field theory for k C in the following method. Let π P be the projection from C to a line l with a center P ∈ 2 . The π P induces an extension field k C /k 1 , where k 1 is a maximal rational subfield. In this paper we study the extension k C /k 1 from several points of view. For example, we consider the following questions: When is the extension k C /k 1 Galois? What is the Galois closure of k C /k 1 ?

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