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Mosc. Math. J., 2014, Volume 14, Number 4, Pages 773–806 (Mi mmj544)  

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

Recursive towers of curves over finite fields using graph theory

Emmanuel Hallouin, Marc Perret

Université Toulouse 2, 5, allées Antonio Machado, 31058 Toulouse cedex, France

Abstract: We give a new way to study recursive towers of curves over a finite field, defined á la Elkies from a bottom curve $X$ and a correspondence $\Gamma$ on $X$. A close examination of singularities leads to a necessary condition for a tower to be asymptotically good. Then, spectral theory on a directed graph, Perron–Frobenius theory and considerations on the class of $\Gamma$ in $\mathrm{NS}(X\times X)$ lead to the fact that, under some mild assumption, a recursive tower can have in some sense only a restricted asymptotic quality. Results are applied to the Bezerra–Garcia–Stichtenoth tower along the paper for illustration.

Key words and phrases: curves over a finite field, curves with many points, graphs, towers of function fields, zeta functions.

DOI: https://doi.org/10.17323/1609-4514-2014-14-4-773-806

Full text: http://www.mathjournals.org/.../2014-014-004-006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 11G20, 14G05, 14G15, 14H20, 5C38, 5C50
Received: December 14, 2012; in revised form March 18, 2014
Language:

Citation: Emmanuel Hallouin, Marc Perret, “Recursive towers of curves over finite fields using graph theory”, Mosc. Math. J., 14:4 (2014), 773–806

Citation in format AMSBIB
\Bibitem{HalPer14}
\by Emmanuel~Hallouin, Marc~Perret
\paper Recursive towers of curves over finite fields using graph theory
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 4
\pages 773--806
\mathnet{http://mi.mathnet.ru/mmj544}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-4-773-806}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3292049}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000349324800006}


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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. E. Hallouin, M. Perret, “A graph aided strategy to produce good recursive towers over finite fields”, Finite Fields Appl., 42 (2016), 200–224  crossref  mathscinet  zmath  isi  scopus
    2. R. Krishnamoorthy, “Correspondences without a core”, Algebr. Number Theory, 12:5 (2018), 1173–1214  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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