SatoTate groups of abelian threefolds: a preview of the classification
Abstract
We announce the classification of SatoTate groups of abelian threefolds over number fields; there are 410 possible conjugacy classes of closed subgroups of USp(6) that occur. We summarize the key points of the "upper bound" aspect of the classification, and give a more rigorous treatment of the "lower bound" by realizing 33 groups that appear in the classification as maximal cases with respect to inclusions of finite index. Further details will be provided in a subsequent paper.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.02071
 Bibcode:
 2019arXiv191102071F
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Group Theory;
 Primary 11M50;
 Secondary 11G10;
 11G20;
 14G10;
 14K15
 EPrint:
 We withdrew the statement that all 33 maximal groups are realizable over Q. To appear in Contemp. Math