8 papers · 1 filter
Supersingular reduction and strongly special intersections in powers of the modular curve
Georgios Papas
We show that Lang--Trotter-type sparsity for simultaneous supersingular reduction of pairs of elliptic curves provides a new arithmetic input for unlikely intersections in powers o…
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…
On the -adic values of G-functions III
Georgios Papas
In this third part in this series we continue from \cite{papaspadicpart1}, the study of relations among values of G-functions associated to a -parameter family of principally po…
On the -adic values of G-functions I
Georgios Papas
This is the first in a series of papers aimed at studying families of G-functions associated to -parameter families of abelian schemes. In particular, the construction of relati…
On the -adic values of G-functions II
Georgios Papas
This is the second paper in a series by the author, centered on the study of values of G-functions associated to a -parameter family of abelian varieties $f:\CX\rightarrow S$ an…
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…