Higher rank subgroups in the class groups of imaginary function fields

Let F be a finite field and T a transcendental element over F . In this paper, we construct, for integers m and n relatively prime to the characteristic of F ( T ) , infinitely many imaginary function fields K of degree m over F ( T ) whose class groups contain subgroups isomorphic to ( Z / n Z ) m...

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Published in:Journal of pure and applied algebra 2006-09, Vol.207 (1), p.51-62
Main Authors: Lee, Yoonjin, Pacelli, Allison M.
Format: Article
Language:English
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Summary:Let F be a finite field and T a transcendental element over F . In this paper, we construct, for integers m and n relatively prime to the characteristic of F ( T ) , infinitely many imaginary function fields K of degree m over F ( T ) whose class groups contain subgroups isomorphic to ( Z / n Z ) m . This increases the previous rank of m − 1 found by the authors in [Y. Lee, A. Pacelli, Class groups of imaginary function fields: The inert case, Proc. Amer. Math. Soc. 133 (2005) 2883–2889].
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2005.09.001