Session S09 - Number Theory in the Americas

Thursday, July 22, 17:00 ~ 17:30 UTC-3

Genus fields of Kummer extensions of rational function fields

Martha Rzedowski

CINVESTAV, IPN, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We obtain the genus field of a general Kummer extension of a global rational function field. First we study the case of a Kummer extension of degree a power of a prime. Then we prove that the genus field of the composite of two abelian extensions of a global rational function field of relatively prime degrees is equal to the composite of the genus fields of the extensions. As a consequence is obtained the genus field of a general Kummer extension.

Joint work with Gabriel Villa (CINVESTAV, IPN, Mexico).

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