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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The divisor classes of the hypersurface $z^{p^{m}}=G(x_{1},\cdots ,x_{n})$ in characteristic $p>0$
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by Jeffrey Lang PDF
Trans. Amer. Math. Soc. 278 (1983), 613-634 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 613-634
  • MSC: Primary 14J05; Secondary 13B10, 14C22
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0701514-1
  • MathSciNet review: 701514