Zheng Xu

collaborators

4 papers

math.NT2023

Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces

Zheng Xu, Yi Ouyang, Zijian Zhou

For two supersingular elliptic curves $E$ and $E^{'}$ defined over $F_{p^{2}}$ , let $[E \times E^{'}]$ be the superspecial abelian surface with the principal polarization $\{0\} \…

math.AG2023

Abundance for threefolds in positive characteristic when $ν = 2$

Zheng Xu

In this paper, we prove the abundance conjecture for threefolds over a perfect field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$ . More precisely,…

math.NT2019

Endomorphism rings of supersingular elliptic curves over $F_{p}$

Songsong Li, Yi Ouyang, Zheng Xu

Let $p > 3$ be a fixed prime. For a supersingular elliptic curve $E$ over $F_{p}$ with $j$ -invariant $j (E) \in F_{p} \ {0, 1728}$ , it is well known that the Fro…

math.NT2019

Neighborhood of the supersingular elliptic curve isogeny graph at $j = 0$ and $1728$

Songsong Li, Yi Ouyang, Zheng Xu

We describe the neighborhood of the vertex $[E_{0}]$ (resp. $[E_{1728}]$ ) in the $ℓ$ -isogeny graph $G_{ℓ} (F_{p^{2}}, - 2 p)$ of supersingular elliptic curves over…

Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces

Abundance for threefolds in positive characteristic when ν=2

Endomorphism rings of supersingular elliptic curves over Fp​

Neighborhood of the supersingular elliptic curve isogeny graph at j=0 and 1728

Abundance for threefolds in positive characteristic when $ν = 2$

Endomorphism rings of supersingular elliptic curves over $F_{p}$

Neighborhood of the supersingular elliptic curve isogeny graph at $j = 0$ and $1728$