Endomorphism algebras of abelian varieties over number fields
Jeudi, 21 Novembre, 2019 - 10:30
A conjecture attributed to Coleman predicts that, if we fix positive integers g and d, then only finitely many isomorphism classes of rings appear as endomorphism rings of abelian varieties of dimension g defined over number fields of degree d. As proved by Rémond, this conjecture implies several other well-known uniformity conjectures about abelian varieties. In this talk, I will discuss links between Coleman's conjecture and other conjectures such as uniform boundedness for Brauer groups of abelian varieties and analogues for K3 surfaces (joint work with Skorobogatov and Zarhin). I will also discuss polynomial bounds for the discriminant of endomorphism rings of abelian varieties, a much stronger statement than Coleman's conjecture, which can be proved in some very special cases and is useful for studying unlikely intersections.
Institution de l'orateur :
Thème de recherche :
Théorie des nombres