### Abstract

Let K be a global function field, oo a degree one prime divisor of K and let A be the Dedekind domain of functions in K regular outside oo. Let H be the Hubert class field of A, B the integral closure of A in H. Let V be a rank one normalized Drinfeld A -module and let β be a prime ideal in B. We explicitly determine the finite A-moduIe structure of Ψ(B/β^{N}). In particular, if K = F_{q}(t), q is an odd prime number and Ψ is the Carlitz F_{q}[t]-module, then the finite F_{q}[t]-module Ψ(F_{q}[t]/β^{N}) is always cyclic.

Original language | English |
---|---|

Pages (from-to) | 1955-1961 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 126 |

Issue number | 7 |

Publication status | Published - 1998 Dec 1 |

### Fingerprint

### Keywords

- Drinfeld modules
- Hubert class field

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*126*(7), 1955-1961.

**Some results on finite drinfeld modules.** / Hsu, Chih-Nung.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 126, no. 7, pp. 1955-1961.

}

TY - JOUR

T1 - Some results on finite drinfeld modules

AU - Hsu, Chih-Nung

PY - 1998/12/1

Y1 - 1998/12/1

N2 - Let K be a global function field, oo a degree one prime divisor of K and let A be the Dedekind domain of functions in K regular outside oo. Let H be the Hubert class field of A, B the integral closure of A in H. Let V be a rank one normalized Drinfeld A -module and let β be a prime ideal in B. We explicitly determine the finite A-moduIe structure of Ψ(B/βN). In particular, if K = Fq(t), q is an odd prime number and Ψ is the Carlitz Fq[t]-module, then the finite Fq[t]-module Ψ(Fq[t]/βN) is always cyclic.

AB - Let K be a global function field, oo a degree one prime divisor of K and let A be the Dedekind domain of functions in K regular outside oo. Let H be the Hubert class field of A, B the integral closure of A in H. Let V be a rank one normalized Drinfeld A -module and let β be a prime ideal in B. We explicitly determine the finite A-moduIe structure of Ψ(B/βN). In particular, if K = Fq(t), q is an odd prime number and Ψ is the Carlitz Fq[t]-module, then the finite Fq[t]-module Ψ(Fq[t]/βN) is always cyclic.

KW - Drinfeld modules

KW - Hubert class field

UR - http://www.scopus.com/inward/record.url?scp=22044452144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22044452144&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22044452144

VL - 126

SP - 1955

EP - 1961

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -