100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

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 : 
Thème de recherche : 
Théorie des nombres
Salle : 
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