Author

Eran Assaf

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Preprint Sep 2026

Exceptional points on Atkin--Lehner quotients

We study the rational points on the star curve $X_0^*(N) := X_0(N)/W(N)$, the quotient of the classical modular curve $X_0(N)$ by the full group of Atkin--Lehner involutions, for squarefree levels $N$. Rational points on $X_0^*(N)$ parameterize $\mathbb{Q}$-curves, i.e.\ elliptic curves $E/\overline{\mathbb{Q}}$ that a...

Eran Assaf, Sachi Hashimoto, A. Shnidman · 0 citations

Preprint Sep 2026

Level structures on tropical abelian varieties

We introduce level structures on tropical abelian varieties and give a modular interpretation of $A_g[m]^{\mathrm{trop}}$, the tropicalization of the moduli space $\mathcal{A}_g[m]$ of principally polarized abelian varieties with level $m$ structure. We study the case of abelian surfaces in greater depth. The link of $...

Eran Assaf, Madeline Brandt, Juliette Bruce et al. · 0 citations