Speaker : Yen-Liang Kuan (National Center for Theoretical Sciences) The Mordell-Weil theorem for t-modules 2020-05-27 (Wed) 11:00 - 12:30 Room 202, Astro-Math. Building For each positive characteristic multiple zeta value (defined by Thakur) $\zeta_A(\mathfrak{s})$, Chang-Papanikolas-Yu constructed the $t$-module $E_{\mathfrak{s}}$ defined over $A$ and integral points $\mathbf{v}_{\mathfrak{s}}$, $\mathbf{u}_{\mathfrak{s}} \in E_{\mathfrak{s}}(A)$. They proved that $\zeta_A(\mathfrak{s})$ is Eulerian (resp. zeta-like) if and only if $\mathbf{v}_{\mathfrak{s}}$ is an $\mathbb{F}_q[t]$-torsion point in $E_{\mathfrak{s}}(A)$ (resp. $\mathbf{v}_{\mathfrak{s}}$, $\mathbf{u}_{\mathfrak{s}}$ are $\mathbb{F}_q[t]$-linearly dependent in $E_{\mathfrak{s}}(A)$). In this talk, we are interested in the structure theory of the $t$-module $E_{\mathfrak{s}}(A)$. Poonen proved an analogue for Drinfeld modules of the Mordell-Weil theorem. We shall generalize his results to the case of specific families of $t$-modules. In particular, we prove that the $t$-module $E_{\mathfrak{s}}(A)$ is the direct sum of its torsion submodule, which is finite, with a free $\mathbb{F}_q[t]$-module of rank $\aleph_0$. ◆Lunch Box Sign Up and Registration: https://reurl.cc/e5jjX7