Some results on finite drinfeld modules

Chih Nung Hsu

doi:10.1090/s0002-9939-98-04337-8

Some results on finite drinfeld modules

Chih Nung Hsu^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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
DOIs	https://doi.org/10.1090/s0002-9939-98-04337-8
Publication status	Published - 1998

Keywords

Drinfeld modules
Hubert class field

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/s0002-9939-98-04337-8

Cite this

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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/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.",

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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

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EP - 1961

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Some results on finite drinfeld modules

Abstract

Keywords

ASJC Scopus subject areas

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