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The divisor classes of the hypersurface $ z\sp{p\sp{m}}=G(x\sb{1},\cdots ,x\sb{n})$ in characteristic $ p>0$

Author: Jeffrey Lang
Journal: Trans. Amer. Math. Soc. 278 (1983), 613-634
MSC: Primary 14J05; Secondary 13B10, 14C22
MathSciNet review: 701514
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Abstract: In this article we use P. Samuel's purely inseparable descent techniques to study the divisor class groups of normal affine hypersurfaces of the form $ {z^p} = G({x_1},\ldots,{x_n})$ and develop an inductive procedure for studying those of the form $ {z^{p^m}} = G$. We obtain results concerning the order and type of these groups and apply this theory to some specific examples.

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Article copyright: © Copyright 1983 American Mathematical Society