Restriction of divisor classes to hypersurfaces in characteristic \(p\) (Q1883041)

Let \(A\) be a Noetherian normal domain of equicharacteristic zero, and let \(f\in A\) be an element such that the ring \(A/fA\) satisfies the condition \(R_1\). \textit{S. Spriroff} defined a map \(\text{Cl}(A)\to \text{Cl}((A/fA)')\) of divisor class groups, where \((A/fA)'\) is the integral closure of \(A/fA\), and gave some conditions for injectivity [J. Pure Appl. Algebra 186, No. 1, 77--89 (2004; Zbl 1095.13009)]. In the paper under review the authors study similar questions in the case of characteristic \(p>0\). In addition, in the case when the ring \(A/fA\) is normal, they also compute quite explicitly the kernel of \(\text{Cl}(A)\to \text{Cl}(A/fA)\) and exhibit examples with non-trivial kernel.