Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Point count divisibility for algebraic sets over ${\mathbb{Z}}/p^\ell{\mathbb{Z}}$ and other finite principal rings

Author(s): Daniel J. Katz
Journal: Proc. Amer. Math. Soc. 137 (2009), 4065-4075.
MSC (2000): Primary 11T06; Secondary 13M10
Posted: July 28, 2009
MathSciNet review: 2538567
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We determine the greatest common divisor of the cardinalities of the algebraic sets generated by collections of polynomials $f_1,\ldots,f_t$ of specified degrees $d_1,\ldots,d_t$ in variables over a finite principal ring . This generalizes the theorems of Ax (, a field), N. M. Katz ( arbitrary, a field), and Marshall-Ramage (, an arbitrary finite principal ring).

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