References of "Lombardo, Davide"
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See detailSome uniform bounds for elliptic curves over Q
Lombardo, Davide; Tronto, Sebastiano UL

E-print/Working paper (2021)

We give explicit uniform bounds for several quantities relevant to the study of Galois representations attached to elliptic curves E/Q. We consider in particular the subgroup of scalars in the image of ... [more ▼]

We give explicit uniform bounds for several quantities relevant to the study of Galois representations attached to elliptic curves E/Q. We consider in particular the subgroup of scalars in the image of Galois, the first Galois cohomology group with values in the torsion of E, and the Kummer extensions generated by points of infinite order in E(Q). [less ▲]

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See detailReductions of points on algebraic groups
Lombardo, Davide; Perucca, Antonella UL

in Journal of the Institute of Mathematics of Jussieu (2019)

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See detailThe 1-eigenspace for matrices in GL2(ℤℓ)
Lombardo, Davide; Perucca, Antonella UL

in New York Journal of Mathematics (2017)

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See detailEffective Kummer Theory for Elliptic Curves
Lombardo, Davide; Tronto, Sebastiano UL

E-print/Working paper (n.d.)

Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform ... [more ▼]

Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])]. When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality [Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α. [less ▲]

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