Cyclotomic units and Stickelberger ideals of global function fields
HTML articles powered by AMS MathViewer
- by Jaehyun Ahn, Sunghan Bae and Hwanyup Jung PDF
- Trans. Amer. Math. Soc. 355 (2003), 1803-1818 Request permission
Abstract:
In this paper, we define the group of cyclotomic units and Stickelberger ideals in any subfield of the cyclotomic function field. We also calculate the index of the group of cyclotomic units in the total unit group in some special cases and the index of Stickelberger ideals in the integral group ring.References
- Jean-Robert Belliard, Sur la structure galoisienne des unités circulaires dans les $\textbf {Z}_p$-extensions, J. Number Theory 69 (1998), no. 1, 16–49 (French, with French summary). MR 1611081, DOI 10.1006/jnth.1997.2200
- Jean-Robert Belliard and Hassan Oukhaba, Sur la torsion de la distribution ordinaire universelle attachée à un corps de nombres, Manuscripta Math. 106 (2001), no. 1, 117–130 (French, with English summary). MR 1860983, DOI 10.1007/s002290100199
- Steven Galovich and Michael Rosen, Units and class groups in cyclotomic function fields, J. Number Theory 14 (1982), no. 2, 156–184. MR 655724, DOI 10.1016/0022-314X(82)90045-2
- Frederick F. Harrop, Circular units of function fields, Trans. Amer. Math. Soc. 341 (1994), no. 1, 405–421. MR 1140916, DOI 10.1090/S0002-9947-1994-1140916-6
- David R. Hayes, Elliptic units in function fields, Number theory related to Fermat’s last theorem (Cambridge, Mass., 1981), Progr. Math., vol. 26, Birkhäuser, Boston, Mass., 1982, pp. 321–340. MR 685307
- David R. Hayes, Stickelberger elements in function fields, Compositio Math. 55 (1985), no. 2, 209–239. MR 795715
- H. Oukhaba, Index formulas for ramified elliptic units, To appear in Compositio Math.
- W. Sinnott, On the Stickelberger ideal and the circular units of a cyclotomic field, Ann. of Math. (2) 108 (1978), no. 1, 107–134. MR 485778, DOI 10.2307/1970932
- W. Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent. Math. 62 (1980/81), no. 2, 181–234. MR 595586, DOI 10.1007/BF01389158
- John Tate, Les conjectures de Stark sur les fonctions $L$ d’Artin en $s=0$, Progress in Mathematics, vol. 47, Birkhäuser Boston, Inc., Boston, MA, 1984 (French). Lecture notes edited by Dominique Bernardi and Norbert Schappacher. MR 782485
- Linsheng Yin, Index-class number formulas over global function fields, Compositio Math. 109 (1997), no. 1, 49–66. MR 1473605, DOI 10.1023/A:1000131711974
- Linsheng Yin, Stickelberger ideals and relative class numbers in function fields, J. Number Theory 81 (2000), no. 1, 162–169. MR 1743498, DOI 10.1006/jnth.1999.2472
- L. Yin, Stickelberger ideals and divisor class numbers. Math. Z. 239 (2002), no. 3, 425–440.
Additional Information
- Jaehyun Ahn
- Affiliation: Department of Mathematics, KAIST Daejon, 305-701, Korea
- Email: jaehyun@mathx.kaist.ac.kr
- Sunghan Bae
- Affiliation: Department of Mathematics, KAIST Daejon, 305-701, Korea
- Email: shbae@math.kaist.ac.kr
- Hwanyup Jung
- Affiliation: Department of Mathematics, KAIST Daejon, 305-701, Korea
- Email: hyjung@mathx.kaist.ac.kr
- Received by editor(s): July 1, 2001
- Received by editor(s) in revised form: October 28, 2002
- Published electronically: January 14, 2003
- Additional Notes: This work was supported by Korea Research Foundation Grant (KRF-2000-015-DP0010)
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 1803-1818
- MSC (2000): Primary 11R58, 11R60
- DOI: https://doi.org/10.1090/S0002-9947-03-03245-8
- MathSciNet review: 1953526