Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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

Author: Daniel J. Katz
Journal: Proc. Amer. Math. Soc. 137 (2009), 4065-4075
MSC (2000): Primary 11T06; Secondary 13M10
Published electronically: July 28, 2009
MathSciNet review: 2538567
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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 $ n$ variables over a finite principal ring $ R$. This generalizes the theorems of Ax ($ t=1$, $ R$ a field), N. M. Katz ($ t$ arbitrary, $ R$ a field), and Marshall-Ramage ($ t=1$, $ R$ an arbitrary finite principal ring).

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Additional Information

Daniel J. Katz
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Received by editor(s): July 10, 2007
Received by editor(s) in revised form: April 26, 2009
Published electronically: July 28, 2009
Additional Notes: This work is in the public domain
Communicated by: Ted Chinburg