26 citations · 103 across the 16 of their papers we have counts for
18 papers
Explicit height bounds for G-functions and unlikely intersections with lines in tori
Martin Orr
This paper computes explicit constants in Bombieri and André's height bound for points at which there are unexpected "global" polymomial relations between values of G-functions. It…
Some new cases of Zilber-Pink in
Christopher Daw, Martin Orr, Georgios Papas
We prove the Zilber-Pink conjecture for curves in that intersect a modular curve in the boundary. We also give an unconditional result for unlikely intersection points hav…
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…
The large Galois orbits conjecture under multiplicative degeneration
Christopher Daw, Martin Orr
We establish the PEL type large Galois orbits conjecture for Hodge generic curves in possessing multiplicative degeneration. Combined with our earlier works, this c…
Zilber-Pink in a product of modular curves assuming multiplicative degeneration
Christopher Daw, Martin Orr
We prove the Zilber--Pink conjecture for curves in whose Zariski closure in passes through the point , going beyond the asymme…
Lattices with skew-Hermitian forms over division algebras and unlikely intersections
Christopher Daw, Martin Orr
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,…
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…
Quantitative reduction theory and unlikely intersections
Christopher Daw, Martin Orr
We prove quantitative versions of Borel and Harish-Chandra's theorems on reduction theory for arithmetic groups. Firstly, we obtain polynomial bounds on the lengths of reduced inte…
Unlikely intersections with CM curves in
Christopher Daw, Martin Orr
The Zilber-Pink conjecture predicts that an algebraic curve in has only finitely many intersections with the special curves, unless it is contained in a proper spec…
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…
On uniformity conjectures for abelian varieties and K3 surfaces
Martin Orr, Alexei N. Skorobogatov, Yuri G. Zarhin
We discuss logical links among uniformity conjectures concerning K3 surfaces and abelian varieties of bounded dimension defined over number fields of bounded degree. The conjecture…
Unlikely intersections with Hecke translates of a special subvariety
Martin Orr
We prove some cases of the Zilber-Pink conjecture on unlikely intersections in Shimura varieties. Firstly, we prove that the Zilber-Pink conjecture holds for intersections between…
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…
Height bounds and the Siegel property
Martin Orr
Let be a reductive group defined over and let be a Siegel set in . The Siegel property tells us that there are only…
On compatibility between isogenies and polarisations of abelian varieties
Martin Orr
We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unli…
Heights of pre-special points of Shimura varieties
Christopher Daw, Martin Orr
Let s be a special point on a Shimura variety, and x a pre-image of s in a fixed fundamental set of the associated Hermitian symmetric domain. We prove that the height of x is poly…
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…