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Fiber products and class groups of hyperelliptic curves
Author(s):
Jeffrey
D.
Achter
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3159-3161.
MSC (2010):
Primary 11R58;
Secondary 11R29, 14H05
Posted:
April 21, 2010
MathSciNet review:
2653940
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Abstract:
Let  be a finite field of odd characteristic, and let  be an odd natural number. An explicit fiber product construction shows that if  divides the class number of some quadratic function field over  , then it does so for infinitely many such function fields.
References:
-
- [Ach06]
- Jeffrey D. Achter, The distribution of class groups of function fields, J. Pure Appl. Algebra 204 (2006), no. 2, 316-333. MR 2184814 (2006h:11132)
- [BJLS08]
- M. Bauer, M. J. Jacobson, Jr., Y. Lee, and R. Scheidler, Construction of hyperelliptic function fields of high three-rank, Math. Comp. 77 (2008), no. 261, 503-530 (electronic). MR 2353964 (2008i:11135)
- [DH89]
- Bert Ditters and Simen J. Hoving, On the connected part of the covariant Tate
 -divisible group and the  -function of the family of hyperelliptic curves  modulo various primes, Math. Z. 200 (1989), no. 2, 245-264. MR 978298 (90e:14047) - [EVW09]
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- [FW89]
- Eduardo Friedman and Lawrence C. Washington, On the distribution of divisor class groups of curves over a finite field, Théorie des nombres (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 227-239. MR 91e:11138
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 -torsion, Manuscripta Math. 117 (2005), no. 3, 299-317. MR 2154252 (2006e:14039) - [Hon66]
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 over a field of characteristic  , Osaka J. Math. 3 (1966), 189-194. MR 0225777 (37:1370) - [Pac09]
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Additional Information:
Jeffrey
D.
Achter
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email:
j.achter@colostate.edu
DOI:
10.1090/S0002-9939-10-10461-4
PII:
S 0002-9939(10)10461-4
Received by editor(s):
December 18, 2009
Posted:
April 21, 2010
Additional Notes:
The author was partially supported by NSA grant H98230-08-1-0051.
Communicated by:
Ken Ono
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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