On explicit descent of marked curves and maps

  title={On explicit descent of marked curves and maps},
  author={Jeroen Sijsling and John Voight},
  journal={Research in Number Theory},
  • Jeroen Sijsling, John Voight
  • Published 2016
  • Mathematics
  • Research in Number Theory
  • We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used to prove this statement in the presence of a smooth point, and in fact these results imply more generally that a marked curve descends to its field of moduli. We give a constructive version of their results, based on an algebraic version of the notion of branches of a morphism and allowing us to extend the… CONTINUE READING