On a problem of Piatetski-Shapiro and Shafarevich

英文摘要：

We revisit a classical paper by Piatetski-Shapiro and Shafarevich on algebraic approach to uniformization and provide a partial solution of the problem, namely, whether the existence of proalgebraic quasi-homogeneous coverings of general type is the characteristic property of algebraic varieties whose universal coverings are bounded symmetric domains.