Abstract: Let $F$ be a number field. Given finitely many $F$-valued points on a commutative algebraic group defined over $F$, a question of interest to number theorists is the determination of the group of their linear relations. In this talk, we investigate an analogous problem in the $t$-module setting. Let $L$ be a global function field, and $E$ be a $d$-dimensional $t$-module defined over $L$. Given finitely many points on $E$ with entries in $L$, we will present an algorithmic approach to compute the module of their $F_q[t]$-linear relations. This is joint work with Wei-Cheng Huang and Changningphaabi Namoijam. 

 

Organizer: Fu-Tsun Wei (NTHU)