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This article is cited in 1 scientific paper (total in 1 paper)
Varieties over finite fields: quantitative theory
S. G. Vlăduţab, D. Yu. Noginb, M. A. Tsfasmancbd a Aix-Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille (I2M, UMR 7373), Marseille, France
b Institute for Information Transmission Problems of Russian Academy of Sciences, Moscow
c CNRS, Laboratoire de Mathématiques de Versailles (UMR 8100), France
d Independent University of Moscow
Abstract:
Algebraic varieties over finite fields are considered from the point of view of their invariants such as the number of points of a variety that are defined over the ground field and its extensions. The case of curves has been actively studied over the last thirty-five years, and hundreds of papers have been devoted to the subject. In dimension two or higher, the situation becomes much more difficult and has been little explored. This survey presents the main approaches to the problem and describes a major part of the known results in this direction.
Bibliography: 102 titles.
Keywords:
algebraic varieties over finite fields, zeta functions, points on surfaces, error-correcting codes, arithmetic statistics, explicit formulae in arithmetic.
Received: 13.11.2017 Revised: 09.01.2018
Citation:
S. G. Vlăduţ, D. Yu. Nogin, M. A. Tsfasman, “Varieties over finite fields: quantitative theory”, Uspekhi Mat. Nauk, 73:2(440) (2018), 75–140; Russian Math. Surveys, 73:2 (2018), 261–322
Linking options:
https://www.mathnet.ru/eng/rm9814https://doi.org/10.1070/RM9814 https://www.mathnet.ru/eng/rm/v73/i2/p75
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Abstract page: | 874 | Russian version PDF: | 185 | English version PDF: | 52 | References: | 81 | First page: | 72 |
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