The Iwasawa main conjecture for semistable abelian varieties over   function fields
  We prove the Iwasawa main conjecture over the arithmetic $\mathbb{Z}_p$-extension for semistable abelian varieties over function fields of characteristic $p>0$. 
King Fai Lai, Ignazio Longhi, Ki-Seng Tan and Fabien Trihan
math.NT