English

Minoration de la hauteur canonique pour les modules de Drinfeld \`a multiplications complexes

Number Theory 2014-08-06 v1

Abstract

Lower Bound for the Canonical Height for Drinfeld Modules with Complex Multiplication. Let K be a fi nite extension of Fq(T), let L=K be a Galois extension with Galois group G and let E be the sub eld of L fixed by the center of G. Assume that there exists a finite place v of K such that the local degrees of E=K above v are bounded. Let ϕ\phi be a Drinfeld module with complex multiplication. We give an e fective lower bound for the canonical height of ϕ\phi on L outside the torsion points of ϕ\phi . In the number field case, this problem was solved by F. Amoroso, S. David and U. Zannier.

Keywords

Cite

@article{arxiv.1408.1019,
  title  = {Minoration de la hauteur canonique pour les modules de Drinfeld \`a multiplications complexes},
  author = {Hugues Bauchère},
  journal= {arXiv preprint arXiv:1408.1019},
  year   = {2014}
}

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