João Paulo Guardieiro

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20202026

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3 papers · 1 filter

math.AG2026

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q + 1} = X^{n} (X^{n} + 1)$

João Paulo Guardieiro, Yuri da Silva, Saeed Tafazolian

We study the algebraic curve over $F_{q^{2}}$ defined by $y^{q + 1} = x^{n} (x^{n} + 1)$ , where $n$ is a positive integer coprime to the characteristic. We first prove (when $q$ is o…

math.AG2025

The ranks of twists of an elliptic curve in characteristic $3$

João Paulo Guardieiro

Starting from the elliptic curve $E : y^{2} = x^{3} - x$ over $F_{9}$ , a curve $X$ over $F_{3^{2 n}}$ and a cyclic cover of $X$ of degree $m \in \{2,3…

math.AG2024

Tate-Shafarevich results for quartic twists in characteristic $2$

Herivelto Borges, João Paulo Guardieiro, Cecília Salgado +1

The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study ellipti…

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve Yq+1=Xn(Xn+1)

The ranks of twists of an elliptic curve in characteristic 3

Tate-Shafarevich results for quartic twists in characteristic 2

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q + 1} = X^{n} (X^{n} + 1)$

The ranks of twists of an elliptic curve in characteristic $3$

Tate-Shafarevich results for quartic twists in characteristic $2$