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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 165–181 (Mi znsl6288)  

This article is cited in 2 scientific papers (total in 2 papers)

Abel pairs and modular curves

D. Oganesyan

Moscow Lomonosov State University
Full-text PDF (908 kB) Citations (2)
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Abstract: We consider rational functions on algebraic curves which have a single zero and a single pole. A pair consisting of such a function and a curve is called Abel pair; a special case of an Abel pair is a Belyi pair. In this paper, we study moduli spaces of Abel pairs for curves of genus one. In particular, we compute a number of Belyi pairs over the fields $\mathbb C$ and $\overline{\mathbb F_p}$. This approach could be fruitfully used for the study of Hurwitz spaces and modular curves for fields of finite characteristics.
Key words and phrases: Belyi pairs, dessins d'enfants, Abel pairs, reduction to positive characteristic, embedded graphs, modular curves, elliptic curves.
Received: 30.04.2016
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 226, Issue 5, Pages 655–666
DOI: https://doi.org/10.1007/s10958-017-3556-4
Bibliographic databases:
Document Type: Article
UDC: 512.772.7+515.179.25
Language: English
Citation: D. Oganesyan, “Abel pairs and modular curves”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 165–181; J. Math. Sci. (N. Y.), 226:5 (2017), 655–666
Citation in format AMSBIB
\Bibitem{Oga16}
\by D.~Oganesyan
\paper Abel pairs and modular curves
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 446
\pages 165--181
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6288}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3520427}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 226
\issue 5
\pages 655--666
\crossref{https://doi.org/10.1007/s10958-017-3556-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029679805}
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  • https://www.mathnet.ru/eng/znsl/v446/p165
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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