On P-adic Uniformization Of Abelian Varieties

This thesis focuses on exploring a new p-adic uniformization of abelian varieties with semistable reduction, called conjugate uniformization. While the case of good reduction has been previously addressed by Iovita–Morrow–Zaharescu through Fontaine integration, we extend their work by introducing a logarithmic version of Fontaine integration, building upon their approach. Under a mild condition, we generalize their main results to abelian varieties with semistable reduction, adapting the techniques employed by Iovita and colleagues. Furthermore, we investigate Raynaud uniformization, identifying a class of abelian varieties that meet the necessary conditions, leading to the uniformization established by Iovita–Morrow–Zaharescu.