Irrationality of Generic Quotient Varieties via Bogomolov Multipliers

Abstract The Bogomolov multiplier of a group is the unramified Brauer associated with quotient variety faithful representation group. This object an obstruction for to be stably rational. purpose this paper study these multipliers nilpotent pro-$p$ groups by transporting them their Lie algebras. Special focus set on case $p$-adic nilpotency class $2$, where we analyse moduli space. then applied give information asymptotic behaviour finite images such exponent $p$. We show that fixed $n$ and increasing $p$, positive proportion order $p^n$ have trivial multipliers. On other hand, fixing $p$ $n$, log-generic non-trivial Whence varieties representations $p$-groups are not rational, applications in non-commutative Iwasawa theory developed.