Effective Methods for Norm-Form Equations

While effective resolution of Thue equations has been well understood since the work of Baker in the 1960s, similar results for norm-form equations in more than two variables have proven difficult to achieve. In 1983, Vojta was able to address the case of three variables over totally complex and Galois number fields. In this paper, we extend his results to effectively resolve several new classes of norm-form equations. In particular, we completely and effectively settle the question of norm-form equations over totally complex Galois sextic fields.Comment: Final version, accepted by Math Annalen. A few changes from the previous version-- in particular there is a new result that also applies over non-Galois extensions. The explicit example was removed and will appear elsewher