Elie Studnia

collaborators

5 papers

math.NT2026

Compactified moduli spaces and Hecke correspondences for elliptic curves with a prescribed $N$ -torsion scheme

Elie Studnia

Given an integer $N \geq 3$ , we prove that for any ring $R$ and any finite locally free commutative $R$ -group scheme $G$ whose geometric fibres are isomorphic to the $N$ -torsion su…

math.NT2026

Arithmetic intersections on non-split Cartan modular curves

Jonathan Love, Elie Studnia, Jan Vonk

Let $p$ be a prime number, and let $I^_{1}, I^_{2} < 0$ be two coprime fundamental discriminants. When $p$ splits in $Q (I^_{1})$ and $Q (I^_{2})$ the height p…

math.NT2026

On obstructions to the Euler system method for Rankin-Selberg convolutions

Elie Studnia

To apply the Euler system method to a $p$ -adic Galois representation $T$ , one needs the existence of a $I ¨ \in G_{Q (I^¼_{p^{\infty}})}$ such that $V / (I ¨ - 1) V$ is free of rank…

math.NT2025

Congruences modulo $23$ to $y^{2} = x^{3} - 23$ are trivial

Elie Studnia

We say that two elliptic curves $E$ and $F$ over $Q$ are congruent modulo a prime $p$ if their $p$ -torsion Galois modules (over the algebraic closure of $Q$ ) are…

math.NT2025

L-functions and rational points for Galois twists of modular curves

Elie Studnia

Let $p$ be an odd prime and $E / Q$ be a rational elliptic curve. There is a smooth affine curve $Y_{E} (p)$ whose rational points parametrize elliptic curves $F / Q$ su…

Compactified moduli spaces and Hecke correspondences for elliptic curves with a prescribed N-torsion scheme

Arithmetic intersections on non-split Cartan modular curves

On obstructions to the Euler system method for Rankin-Selberg convolutions

Congruences modulo 23 to y2=x3−23 are trivial

L-functions and rational points for Galois twists of modular curves

Compactified moduli spaces and Hecke correspondences for elliptic curves with a prescribed $N$ -torsion scheme

Congruences modulo $23$ to $y^{2} = x^{3} - 23$ are trivial