D. Lombardo

activity

20152026

most citedGalois representations attached to abelian varieties of CM type

3 citations · 3 across the 9 of their papers we have counts for

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Showing 2026 · math.NTShow all

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math.NT2026

Interpolation determinants and the Lebesgue--Nagell equation $a^{2} - D = b^{p}$

Davide Lombardo

We prove the long-standing conjecture that, for every odd prime $p$ , the only integral solutions of $a^{2} - 2 = b^{p}$ are $(a, b) = (\pm 1, - 1)$ . We also completely solve the analogous equa…

math.NT2026

Equationless quadratic Chabauty for non-split Cartan modular curves

Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2

The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve $X_{ns}^{+} (N)$ of prime level $N ⩾ 13$ .…

math.NT2026

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Matthew Bisatt, Lorenzo Furio, Davide Lombardo

Let $E / Q_{p}$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$ -adic images of $E$ using too…

Interpolation determinants and the Lebesgue--Nagell equation a2−D=bp

Equationless quadratic Chabauty for non-split Cartan modular curves

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Interpolation determinants and the Lebesgue--Nagell equation $a^{2} - D = b^{p}$