3 citations · 3 across the 11 of their papers we have counts for
11 papers
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…
-functions and quaternionic multiplication in
Georgios Papas
We consider -functions associated with one--parameter families of principally polarized abelian surfaces. We construct relations among their values at QM points, under the assum…
On the -adic values of -functions
Georgios Papas
We study -functions centered at smooth fibers of one--parameter families of principally polarized abelian varieties. Building on work of Yves André, we associate to such familie…
Local values of G-functions at CM points
Georgios Papas
We study G-functions attached to one--parameter families of elliptic curves centered at a CM point. Using de Rham--Betti and de Rham--crystalline period matrices, we construct non-…
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…
Zilber-Pink in : Beyond multiplicative degeneration
Georgios Papas
We establish Large Galois orbits conjectures for points of unlikely intersections of curves in , upon assumptions on the intersection of such curves with the boundary $X(1)…
Effective Brauer-Siegel on some curves in
Georgios Papas
We establish an effective version of Siegel's lower bounds for class numbers of imaginary quadratic fields in certain cures in . Our proof goes through the G-functions meth…
Some cases of the Zilber-Pink conjecture for curves in
Georgios Papas
Following our work in \cite{papas2022height}, we extend the height bounds established by Y. André in his seminal research monograph \cite{andre1989g} for -parameter families of…
Unlikely intersections in the Torelli locus and the G-functions method
Georgios Papas
Consider a smooth irreducible Hodge generic curve defined over $\bar{\Q}$ in the Torelli locus . We establish Zilber-Pink-type statements for such cur…
Ax-Schanuel for
Georgios Papas
In this paper we prove an Ax-Schanuel type result for the exponential functions for general linear groups over . We prove the result first for the group of upper triang…