• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.349-357
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• 1995

In the theory of elliptic curves over a complete field with bad reduction (i.e. with nonintegral j-invariant) Tate elliptic curves play an important role. Likewise, in the theory of Drinfeld modules, Tate-Drinfeld modules replace Tate elliptic curves.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-257
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• 1995

In the catagory of t-modules the Carlitz module C plays the role of $G_m$ in the category of group schemes. For a finite t-module G which corresponds to a finite group scheme, Taguchi [T] showed that Hom (G, C) is the "right" dual in the category of finite- t-modules which corresponds to the Cartier dual of a finite group scheme. In this paper we show that for Drinfeld modules (i.e., t-modules of dimension 1) of rank 2 there is a natural way of defining its dual by using the extension of drinfeld module by the Carlitz module which is in the same vein as defining the dual of an abelian varietiey by its $G_m$-extensions. Our results suggest that the extensions are the right objects to define the dual of arbitrary t-modules.t-modules.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.85-90
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• 1991

In this article we introduce the readers to the theory of Carlitz modules which are rank one Drinfeld modules. The main point is the striking similarities between cyclotomic number fields and Carlitz modules.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.743-749
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• 1998

On the group of all extensions of elliptic modules by the Carlitz module we define Frobenius map and by using a concrete description of the extension group we give an explicit description of the Frobenius map.