Skip to main content Accessibility help
×
Home
Hostname: page-component-79b67bcb76-jn9wc Total loading time: 0.214 Render date: 2021-05-14T21:53:32.094Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

genus theory for function fields

Published online by Cambridge University Press:  09 April 2009

Sunghan Bae
Affiliation:
Department of MathematicsKorea Advanced Institute of Science and TechnologyTaejon, 305–701, Korea
Ja Kyung Koo
Affiliation:
Department of MathematicsKorea Advanced Institute of Science and TechnologyTaejon, 305–701, Korea
Rights & Permissions[Opens in a new window]

Abstract

We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Clement, R., ‘The genus field of an algebraic function field’, J. Number Theory 40 (1992), 359375.CrossRefGoogle Scholar
[2]Fröhlich, A., Central extensions, Galois groups, and ideal class groups of number fields, Contemp. Math. 24 (Amer. Math. Soc., Providence, 1983).CrossRefGoogle Scholar
[3]Hasse, H., ‘Zur Geschlecht Theorie in quadratischen Zahlkörpern’, J. Math. Soc. Japan 3 (1951), 4551.CrossRefGoogle Scholar
[4]Hayes, D., ‘Explicit class field theory for rational function fields’, Trans. Amer. Math. Soc. 189 (1974), 7791.CrossRefGoogle Scholar
[5]Hayes, D., ‘Stickelberger elements in function fields’, Compositio Math. 55 (1985), 209239.Google Scholar
[6]Rosen, M., ‘The Hilbert class field in function fields’, Exposition. Math. 5 (1987), 365378.Google Scholar
You have Access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

genus theory for function fields
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

genus theory for function fields
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

genus theory for function fields
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *