Abstract
In this paper we prove that complete families of smooth and projective curves of genus g≥2 in characteristic p>0 with a constant geometric fundamental group are isotrivial.
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Saïdi, M. On complete families of curves with a given fundamental group in positive characteristic. manuscripta math. 118, 425–441 (2005). https://doi.org/10.1007/s00229-005-0592-z
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DOI: https://doi.org/10.1007/s00229-005-0592-z