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Unramified graph covers of finite degree

By Winnie Li

Appears in collections : Dynamics and graphs over finite fields: algebraic, number theoretic and algorithmic aspects / Dynamique et graphes sur les corps finis : aspects algebriques, arithmétiques et algorithmiques, Exposés de recherche

Given a finite connected undirected graph $X$, its fundamental group plays the role of the absolute Galois group of $X$. The familiar Galois theory holds in this setting. In this talk we shall discuss graph theoretical counter parts of several important theorems for number fields. Topics include (a) Determination, up to equivalence, of unramified normal covers of $X$ of given degree, (b) Criteria for Sunada equivalence, (c) Chebotarev density theorem. This is a joint work with Hau-Wen Huang.

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Citation data

  • DOI 10.24350/CIRM.V.18951603
  • Cite this video Li Winnie (3/30/16). Unramified graph covers of finite degree. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18951603
  • URL https://dx.doi.org/10.24350/CIRM.V.18951603

Bibliography

  • Cassels, J.W.S. (Ed.), & Fröhlich, A. (Ed.). (2010). Algebraic number theory. London: London Mathematical Society
  • Huang, H-W., & Li, W. Unramified graph covers of finite degree, preprint, 2015
  • Somodi, M. (2015). On Sunada equivalent graph coverings. Journal of Combinatorics and Number Theory, 7(2)
  • A. Terras, Zeta Functions of Graphs: A Stroll through the Garden. Cambridge Studies in Advanced Mathematics, vol. 128 (2010) - http://bibli.cirm-math.fr/Record.htm?idlist=1&record=19271403124910996859

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