We give a complete answer to the local-global divisibility problem for algebraic tori. In particular, we prove that given an odd prime p, if T is an algebraic torus of dimension r p-1. Finally, we prove that under certain hypotheses on the number field generated by the coordinates of the p^n-torsion points of T, the local-global divisibility still holds for tori of dimension less than 3(p-1).
Local–global divisibility on algebraic tori
Alessandri Jessica
Writing – Original Draft Preparation
;
2024-01-01
Abstract
We give a complete answer to the local-global divisibility problem for algebraic tori. In particular, we prove that given an odd prime p, if T is an algebraic torus of dimension r p-1. Finally, we prove that under certain hypotheses on the number field generated by the coordinates of the p^n-torsion points of T, the local-global divisibility still holds for tori of dimension less than 3(p-1).File in questo prodotto:
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