27 citations · 62 across the 19 of their papers we have counts for
19 papers
Lang-Trotter phenomena and unlikely intersections
Christopher Daw, Georgios Papas
We show that the Lang-Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber-Pink conjecture for curves in . Unlike previous results for cur…
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…
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…
A note on unlikely intersections in Shimura varieties
Vahagn Aslanyan, Christopher Daw
We discuss the relationships between the André-Oort, André-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pi…
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,…
Modular curves and their pseudo-analytic cover
Boris Zilber, Chris Daw
We find a natural -axiomatisation of a structure on the upper half-plane as the covering space of modular curves. The main theorem states that has a…
Canonical models of modular curves and the Galois action on CM-points
Boris Zilber, Chris Daw
We use the theory of canonical models of Shimura varieties to describe the projective limit of the curves Y(N), all N, and its automorphism group. In particular we prove that the G…
Effective computations for weakly optimal subvarieties
Gal Binyamini, Christopher Daw
Ren and the second author established that the weakly optimal subvarieties (e.g. maximal weakly special subvarieties) of a subvariety of a Shimura variety arise in finitely man…
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…
The space of homogeneous probability measures on is compact
Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo +1
In this paper we prove that the space of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space is compact. As an applicat…
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…
Effective estimates for the degrees of maximal special subvarieties
Christopher Daw, Ariyan Javanpeykar, Lars Kühne
Let be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special sub…
Convergence of measures on compactifications of locally symmetric spaces
Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo
We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space is compact. More…
Conjugation of semisimple subgroups over real number fields of bounded degree
Mikhail Borovoi, Christopher Daw, Jinbo Ren
Let be a linear algebraic group over a field of characteristic 0. We show that any two connected semisimple -subgroups of that are conjugate over an algebraic closur…
Applications of the hyperbolic Ax-Schanuel conjecture
Christopher Daw, Jinbo Ren
In 2014, Pila and Tsimerman gave a proof of the Ax-Schanuel conjecture for the -function and, with Mok, have recently announced a proof of its generalization to any (pure) Shimu…
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…
The André-Oort conjecture via o-minimality
Christopher Daw
The purpose of this article is to explain the Pila-Zannier strategy for proving the André-Oort conjecture. First, however, we will provide a brief introduction to the theory of Shi…
Categoricity of modular and Shimura curves
Christopher Daw, Adam Harris
We describe a model-theoretic setting for the study of Shimura varieties, and study the interaction between model theory and arithmetic geometry in this setting. In particular, we…