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Fundam. Prikl. Mat., 2005, Volume 11, Issue 2, Pages 25–43 (Mi fpm823)  

This article is cited in 3 scientific papers (total in 3 papers)

Prime numbers of bad reduction for dessins of genus 0

A. M. Vashevnik

M. V. Lomonosov Moscow State University

Abstract: This article expands the special case of the Grothendieck theory to arbitrary fields. A formal definition of Belyi function over an arbitrary field is introduced. It turns out that the properties of Belyi functions over finite fields and the properties of classical Belyi functions are quite different. A definition of the primes of bad reduction is also given, and the primes of bad reduction are calculated for some dessin families.

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English version:
Journal of Mathematical Sciences (New York), 2007, 142:2, 1883–1894

Bibliographic databases:

UDC: 512.624.3

Citation: A. M. Vashevnik, “Prime numbers of bad reduction for dessins of genus 0”, Fundam. Prikl. Mat., 11:2 (2005), 25–43; J. Math. Sci., 142:2 (2007), 1883–1894

Citation in format AMSBIB
\Bibitem{Vas05}
\by A.~M.~Vashevnik
\paper Prime numbers of bad reduction for dessins of genus~0
\jour Fundam. Prikl. Mat.
\yr 2005
\vol 11
\issue 2
\pages 25--43
\mathnet{http://mi.mathnet.ru/fpm823}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2157927}
\zmath{https://zbmath.org/?q=an:1073.14043}
\transl
\jour J. Math. Sci.
\yr 2007
\vol 142
\issue 2
\pages 1883--1894
\crossref{https://doi.org/10.1007/s10958-007-0095-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33947356280}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Dremov, A. M. Vashevnik, “On Belyi pairs over arbitrary fields”, J. Math. Sci., 149:3 (2008), 1187–1190  mathnet  crossref  mathscinet  zmath
    2. George B. Shabat, “Visualizing Algebraic Curves: from Riemann to Grothendieck”, Zhurn. SFU. Ser. Matem. i fiz., 1:1 (2008), 42–51  mathnet  elib
    3. D. A. Oganesyan, “Zolotarev polynomials and reduction of Shabat polynomials into a positive characteristic”, Moscow University Mathematics Bulletin, 71:6 (2016), 248–252  mathnet  crossref  mathscinet  isi
  • Фундаментальная и прикладная математика
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