Jiangwei Xue

activity

20092026

most citedSupersingular abelian surfaces and Eichler class number formula

4 citations · 19 across the 24 of their papers we have counts for

collaborators

24 papers

math.NT2026

Ribet bimodules and principally polarized superspecial abelian varieties with quaternion action

Jiangwei Xue, Xiangning Yang

In an influential paper [K. Ribet, Bimodules and abelian surfaces, in Algebraic number theory, 359-407, Adv. Stud. Pure Math., Vol. 17, 1989] on the bad reduction of Shimura curves…

math.NT2026

Superspecial Points on Shimura Curves

Yasuhiro Terakado, Jiangwei Xue, Chia-Fu Yu

Let $X$ be the Shimura curve attached to an indefinite quaternion $Q$ -algebra $B$ with a maximal order $O_{B}$ . This paper investigates the reduction $X \otimes F_{p}$ …

math.NT2026

Polarized superspecial abelian varieties over $F_{p}$ via hermitian lattices

Yucui Lin, Jiangwei Xue, Chia-Fu Yu

We study the set of isomorphism classes of polarized superspecial abelian varieties $(A, λ)$ of a fixed dimension over $F_{p}$ with Frobenius endomorphism $π_{A} = - p$ and…

math.NT2023

On the supersingular locus of Shimura varieties for quaternionic unitary groups

Yasuhiro Terakado, Jiangwei Xue, Chia-Fu Yu

We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a…

math.NT2022

Optimal spinor selectivity for quaternion orders

Jiangwei Xue, Chia-Fu Yu

Let $D$ be a quaternion algebra over a number field $F$ , and $G$ be an arbitrary genus of $O_{F}$ -orders of full rank in $D$ . Let $K$ be a quadratic field extension of $F$ …

math.NT2022

On $F_{p}$ -roots of the Hilbert class polynomial modulo $p$

Mingjie Chen, Jiangwei Xue

The Hilbert class polynomial $H_{O} (x) \in Z [x]$ attached to an order $O$ in an imaginary quadratic field $K$ is the monic polynomial whose roots are pr…

math.NT2021★ 1 cited

On superspecial abelian surfaces over finite fields III

Jiangwei Xue, Chia-Fu Yu, Yuqiang Zheng

In the paper [On superspecial abelian surfaces over finite fields II. J. Math. Soc. Japan, 72(1):303--331, 2020], Tse-Chung Yang and the first two current authors computed explicit…

math.NT2020

Optimal spinor selectivity for quaternion Bass orders

Deke Peng, Jiangwei Xue

Let $A$ be a quaternion algebra over a number field $F$ , and $O$ be an $O_{F}$ -order of full rank in $A$ . Let $K$ be a quadratic field extension of $F$ that embeds into $A$ …

math.NT2020★ 2 cited

Polarized superspecial simple abelian surfaces with real Weil numbers

Jiangwei Xue, Chia-Fu Yu

Let $q$ be an odd power of a prime $p \in N$ , and $PPSP (q)$ be the finite set of isomorphism classes of principally polarized superspecial abelian surfaces…

math.NT2019★ 1 cited

Trace formulas for the norm one group of totally definite quaternion algebras

Jiangwei Xue, Chia-Fu Yu

In his pioneering work [Crelle's Journal, 1955], Eichler established the theory of trace formulas for Brandt matrices of quaternion orders. From it he derived a class number formul…

math.NT2018★ 1 cited

On superspecial abelian surfaces and type numbers of totally definite quaternion algebras

Jiangwei Xue, Chia-Fu Yu

In this paper we determine the number of endomorphism rings of superspecial abelian surfaces over a field $F_{q}$ of odd degree over $F_{p}$ in the isogeny class corr…

math.NT2018★ 3 cited

Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields

Qun Li, Jiangwei Xue, Chia-Fu Yu

We study a form of refined class number formula (resp. type number formula) for maximal orders in totally definite quaternion algebras over real quadratic fields, by taking into co…

math.NT2018★ 1 cited

On superspecial abelian surfaces over finite fields II

Jiangwei Xue, Tse-Chung Yang, Chia-Fu Yu

Extending the results of [Asian J. Math. 2019], in [Doc. Math. \textbf{21}, 2016] we calculated explicitly the number of isomorphism classes of superspecial abelian surfaces over a…

math.NT2018

On counting certain abelian varieties over finite fields

Jiangwei Xue, Chia-Fu Yu

This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit for…

math.NT2016

Numerical Invariants of Totally Imaginary Quadratic $Z [p]$ -orders

Jiangwei Xue, Tse-Chung Yang, Chia-Fu Yu

Let $A$ be a real quadratic order of discriminant $p$ or $4 p$ with a prime $p$ . In this paper we classify all proper totally imaginary quadratic $A$ -orders $B$ with index $w(B)=[B^…

math.NT2016★ 1 cited

On superspecial abelian varieties over finite fields

Jiangwei Xue, Tse-Chung Yang, Chia-Fu Yu

In this paper we establish a new lattice description for superspecial abelian varieties over a finite field $F_{q}$ of $q = p^{a}$ elements. Our description depends on the pari…

math.NT2014★ 4 cited

Supersingular abelian surfaces and Eichler class number formula

Jiangwei Xue, Tse-Chung Yang, Chia-Fu Yu

Let $F$ be a totally real field with ring of integers $O_{F}$ , and $D$ be a totally definite quaternion algebra over $F$ . A well-known formula established by Eichler and then extende…

math.NT2013

Abelian varieties without a prescribed Newton Polygon reduction

Jiangwei Xue, Chia-Fu Yu

In this article we construct for each integer $n \geq 2$ an abelian variety $A$ of dimension $n$ defined over a number field for which there exists a symmetric slope sequence of leng…

math.AG2013

Fixed points and homology of superelliptic Jacobians

Haining Wang, Jiangwei Xue, Chia-Fu Yu

Let $η : C_{f, N} \to P^{1}$ be a cyclic cover of $P^{1}$ of degree $N$ which is totally and tamely ramified for all the ramification points. We determine the group of f…

math.NT2013★ 1 cited

Endomorphism algebras of factors of certain hypergeometric Jacobians

Jiangwei Xue, Chia-Fu Yu

We classify the endomorphism algebras of factors of the Jacobian of certain hypergeometric curves over a field of characteristic zero. Other than a few exceptional cases, the endom…

math.AG2011

Hodge Groups of certain Superelliptic Jacobians II

Jiangwei Xue

Let K be a field of characteristic zero, f(x) be a polynomial with coefficients in K and without multiple roots. We consider the superelliptic curve C_{f,q} defined by y^q=f(x), wh…

math.AG2009★ 1 cited

Hodge groups of certain superelliptic jacobians

Jiangwei Xue, Yuri G. Zarhin

Suppose that $K$ is a field of characteristic 0, $p$ is an odd prime, $r$ a positive integer, $q = p^{r}$ a prime power. Suppose that $f (x)$ is a polynomial of degree $n > 4$ with coef…

math.AG2009★ 1 cited

Centers of Hodge groups of superelliptic jacobians

Jiangwei Xue, Yuri G. Zarhin

We give lower bounds for dimensions of the centers of Hodge groups of superelliptic jacobians. In "generic case" this bound is precise. We also discuss dimensions of simple abelian…

math.AG2009★ 2 cited

Endomorphism algebras of Jacobians of certain superelliptic curves

Jiangwei Xue

Let $p$ be a prime, and $q$ a power of $p$ . Using Galois theory, we show that over a field $K$ of characteristic zero, the endomorphism algebras of the jacobians of certain superel…

Ribet bimodules and principally polarized superspecial abelian varieties with quaternion action

Superspecial Points on Shimura Curves

Polarized superspecial abelian varieties over Fp​ via hermitian lattices

On the supersingular locus of Shimura varieties for quaternionic unitary groups

Optimal spinor selectivity for quaternion orders

On Fp​-roots of the Hilbert class polynomial modulo p

On superspecial abelian surfaces over finite fields III

Optimal spinor selectivity for quaternion Bass orders

Polarized superspecial simple abelian surfaces with real Weil numbers

Trace formulas for the norm one group of totally definite quaternion algebras

On superspecial abelian surfaces and type numbers of totally definite quaternion algebras

Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields

On superspecial abelian surfaces over finite fields II

On counting certain abelian varieties over finite fields

Numerical Invariants of Totally Imaginary Quadratic Z[p​]-orders

On superspecial abelian varieties over finite fields

Supersingular abelian surfaces and Eichler class number formula

Abelian varieties without a prescribed Newton Polygon reduction

Fixed points and homology of superelliptic Jacobians

Endomorphism algebras of factors of certain hypergeometric Jacobians

Hodge Groups of certain Superelliptic Jacobians II

Hodge groups of certain superelliptic jacobians

Centers of Hodge groups of superelliptic jacobians

Endomorphism algebras of Jacobians of certain superelliptic curves

Polarized superspecial abelian varieties over $F_{p}$ via hermitian lattices

On $F_{p}$ -roots of the Hilbert class polynomial modulo $p$

Numerical Invariants of Totally Imaginary Quadratic $Z [p]$ -orders