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# Martin Orr

Endomorphism algebras of abelian varieties over number fields
Jeudi, 21 Novembre, 2019 - 10:30
Résumé :
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 :
Warwick
Thème de recherche :
Théorie des nombres
Salle :
SALLE 4