Recovering algebraic curves from L-functions of Hilbert class fields

In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its constant field extensions. As a consequence, we give a new proof of a result of Mochizuki and Tamagawa that two such curv...

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Veröffentlicht in:	Research in number theory 2020-12, Vol.6 (4), Article 43
Hauptverfasser:	Booher, Jeremy, Voloch, José Felipe
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Sprache:	eng
Schlagworte:	Fields (mathematics) Mathematics Mathematics and Statistics Number Theory
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description	In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its constant field extensions. As a consequence, we give a new proof of a result of Mochizuki and Tamagawa that two such curves with isomorphic fundamental groups are themselves isomorphic.
doi_str_mv	10.1007/s40993-020-00222-0
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title	Recovering algebraic curves from L-functions of Hilbert class fields
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