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NCTS Seminar on Number Theory
13:30 - 14:30, October 23, 2019 (Wednesday)
Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
The Mordell-Weil Theorem for T-modules
Yen-Liang Kuan (NCTS)


In 1995, Poonen proved an analogue for Drinfeld modules of the Mordell-Weil theorem. In this talk, we shall generalize his results to the case of -modules. Specifically, let be a -module defined over a finite extension of the fraction field of . Assume that there is an integer such that
with and the matrix is invertible. Then the -module is the direct sum of its torsion submodule, which is finite, with a free -module of rank . Moreover, we also show that the -th tensor power of the Carlitz module is a direct sum of of a free -module of rank and a finite torsion module.


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