Abstract
The injectivity of the restriction homomorphism on divisor class groups to hypersurfaces has been studied by Grothendieck, Danilov, Lipman, and Griffith & Weston, among others. In particular, when A is a Noetherian normal domain of equicharacteristic zero and A/ fA satisfies R 1, Spiroff established a map Cl( A)→Cl(( A/ fA)′), where ( A/ fA)′ represents the integral closure of A/ fA, and gave some conditions for injectivity. In this paper, the authors continue in the same vein, but in the case of characteristic p>0. In addition, when the hypersurface A/ fA is normal, they provide further enlightenment about the kernel of Cl( A)→Cl( A/ fA). Finally, using the second author's previous results, they exhibit a new class of examples for which the kernel is non-trivial.
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