Class groups of global function fields with certain splitting behaviors of the infinite prime

Author:
Yoonjin Lee

Journal:
Proc. Amer. Math. Soc. **137** (2009), 415-424

MSC (2000):
Primary 11R29; Secondary 11R58

DOI:
https://doi.org/10.1090/S0002-9939-08-09581-6

Published electronically:
October 6, 2008

MathSciNet review:
2448559

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Abstract: For certain two cases of splitting behaviors of the prime at infinity with unit rank , given positive integers , we construct infinitely many global function fields such that the ideal class group of of degree over has -rank at least and the prime at infinity splits in as given, where denotes a finite field and a transcendental element over . In detail, for positive integers , and with and a given signature , , such that , in the following two cases where is arbitrary and for each , or and 's are the same for each , we construct infinitely many global function fields of degree over such that the ideal class group of contains a subgroup isomorphic to and the prime at infinity splits into primes in with and for (so, is of unit rank ).

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Additional Information

**Yoonjin Lee**

Affiliation:
Department of Mathematics, Ewha Womans University, Seoul, 120-750, Republic of Korea

Email:
yoonjinl@ewha.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-08-09581-6

Keywords:
Class group,
class number,
rank of class group,
imaginary function field

Received by editor(s):
April 26, 2007

Published electronically:
October 6, 2008

Additional Notes:
This work was supported by the Ewha Womans University Research Grant of 2007

Communicated by:
Wen-Ching Winnie Li

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.