Point count divisibility for algebraic sets over ${\mathbb {Z}}/p^\ell {\mathbb {Z}}$ and other finite principal rings
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- by Daniel J. Katz
- Proc. Amer. Math. Soc. 137 (2009), 4065-4075
- DOI: https://doi.org/10.1090/S0002-9939-09-10017-5
- Published electronically: July 28, 2009
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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).References
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Bibliographic Information
- Daniel J. Katz
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 787969
- Email: katz.daniel.j@gmail.com
- 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
- Journal: Proc. Amer. Math. Soc. 137 (2009), 4065-4075
- MSC (2000): Primary 11T06; Secondary 13M10
- DOI: https://doi.org/10.1090/S0002-9939-09-10017-5
- MathSciNet review: 2538567