Some results on finite Drinfeld modules

Author:
Chih-Nung Hsu

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1955-1961

MSC (1991):
Primary 11G09; Secondary 11A05

DOI:
https://doi.org/10.1090/S0002-9939-98-04337-8

MathSciNet review:
1451807

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a global function field, a degree one prime divisor of and let be the Dedekind domain of functions in regular outside . Let be the Hilbert class field of , the integral closure of in . Let be a rank one normalized Drinfeld -module and let be a prime ideal in . We explicitly determine the finite -module structure of . In particular, if , is an odd prime number and is the Carlitz -module, then the finite -module is always cyclic.

**1.**E. -U. Gekeler `Drinfeld Modular Curves', LNM 1231, Springer-Verlag (1986). MR**88b:11077****2.**E. -U. Gekeler `On finite Drinfeld Modules', J. Algebra 141 (1991), pp. 187-203. MR**92e:11064****3.**David Goss `Basic Structures of Function Field Arithmetic', Springer-Verlag (1996). CMP**97:05****4.**D. R. Hayes `Explicit class field theory for ration function fields', Transations of the American Mathematical Society, vol 189 (1974), pp. 77 - 91. MR**48:8444****5.**D. R. Hayes `A Brief introduction to Drinfeld modules', in `The Arithmetic of Function Fields' (edited by D. Goss, D. R. Hayes and M. I. Rosen), (1992), pp. 1-32. MR**93m:11050****6.**K. Ireland and M. Rosen `A Classical Introduction to Modern Number Theory', Springer-Verlag. MR**92e:11001****7.**J. K. Yu `Isogenies of Drinfeld modules over finite fields', J. Number Theory 54 (1995), pp. 161-171. MR**96i:11060**

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Additional Information

**Chih-Nung Hsu**

Affiliation:
Department of Mathematics, National Taiwan Normal University, 88 Sec. 4 Ting-Chou Road, Taipei, Taiwan

Email:
maco@math.ntnu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-98-04337-8

Keywords:
Drinfeld modules,
Hilbert class field

Received by editor(s):
July 23, 1996

Received by editor(s) in revised form:
December 26, 1996

Communicated by:
William W. Adams

Article copyright:
© Copyright 1998
American Mathematical Society