3 problems

Let $R$ be a local valuation ring with fraction field $K$, let $G$ be a finite group, and let $\Lambda$ be a Hopf order in $K[G]$. Write $G_0^R(\Lambda)$ for the relevant Grothendi…

Let $R$ be the valuation ring of a finite extension $K$ of $\mathbb Q_p$, let $G$ be a finite group, and let $A^D$ be a Hopf $R$-order in $K[G]$. Define the extension-of-scalars ma…

Let $R$ be a complete discrete valuation ring of characteristic $p>0$, with fraction field $K$, and let $n$ be a positive integer. Consider Hopf orders in cyclic group rings of ran…