26 citations · 103 across the 16 of their papers we have counts for
6 papers · 1 filter
Extension of relative rigid homomorphisms from the formal multiplicative group
Martin Orr
A theorem of Lütkebohmert states that a rigid group homomorphism from the formal multiplicative group to a smooth commutative rigid group , with relatively compact image, can be…
Invariant Brauer group of an abelian variety
Martin Orr, Alexei N. Skorobogatov, Domenico Valloni +1
We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers…
Galois conjugates of special points and special subvarieties in Shimura varieties
Martin Orr
Let be a Shimura variety with reflex field . We prove that the action of on maps special points to special points and speci…
Finiteness theorems for K3 surfaces and abelian varieties of CM type
Martin Orr, Alexei N. Skorobogatov
We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism…
Families of abelian varieties with many isogenous fibres
Martin Orr
Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points…
Lower bounds for ranks of Mumford-Tate groups
Martin Orr
Let A be a complex abelian variety and G its Mumford--Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank…