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)

Abstract:

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.