Recovering algebraic curves from L-functions of Hilbert class fields
Number Theory
2020-10-08 v3 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2003.10597,
title = {Recovering algebraic curves from L-functions of Hilbert class fields},
author = {Jeremy Booher and José Felipe Voloch},
journal= {arXiv preprint arXiv:2003.10597},
year = {2020}
}
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