Lattices with skew-Hermitian forms over division algebras and unlikely intersections

Daw, C. ORCID: https://orcid.org/0000-0002-2488-6729 and Orr, M. (2023) Lattices with skew-Hermitian forms over division algebras and unlikely intersections. Journal de l'École polytechnique — Mathématiques, 10. pp. 1097-1156. ISSN 2270-518X doi: 10.5802/jep.240

Abstract/Summary

This paper has two objectives. First, we study lattices with skew-Hermitian forms over division algebras with positive involutions. For division algebras of Albert types I and II, we show that such a lattice contains an “orthogonal” basis for a sublattice of effectively bounded index. Second, we apply this result to obtain new results in the field of unlikely intersections. More specifically, we prove the Zilber–Pink conjecture for the intersection of curves with special subvarieties of simple PEL type I and II under a large Galois orbits conjecture. We also prove this Galois orbits conjecture for certain cases of type II.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/111964
Identification Number/DOI	10.5802/jep.240
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	École Polytechnique
Download/View statistics	View download statistics for this item