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 curves with isomorphic fundamental groups are themselves isomorphic.

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Correspondence to José Felipe Voloch.

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The authors were supported by the Marsden Fund Council administered by the Royal Society of New Zealand. They would also like to thank Jakob Stix and the referees for many helpful comments.

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Booher, J., Voloch, J.F. Recovering algebraic curves from L-functions of Hilbert class fields. Res. number theory 6, 43 (2020).

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  • L-functions
  • Curves over finite fields
  • Fundamental groups