M. Stoll

activity

19992025

most citedThe Cassels-Tate pairing on polarized abelian varieties

179 citations · 759 across the 49 of their papers we have counts for

collaborators

53 papers

math.AG2025

The valuation of the discriminant of a hypersurface

Bjorn Poonen, Michael Stoll

Let $R$ be a discrete valuation ring, with valuation $v : R ↠ Z_{\geq 0} \cup {\infty}$ and residue field $k$ . Let $H$ be a hypersurface $\operatorn…

math.NT2023

The Cassels-Tate pairing on 2-Selmer groups of elliptic curves

Himanshu Shukla, Michael Stoll

We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This lead…

math.NT2022

Dynamics of quadratic polynomials and rational points on a curve of genus $4$

Hang Fu, Michael Stoll

Let $f_{t} (z) = z^{2} + t$ . For any $z \in Q$ , let $S_{z}$ be the collection of $t \in Q$ such that $z$ is preperiodic for $f_{t}$ . In this article, assuming a well-known conject…

math.NT2021★ 3 cited

Minimization of hypersurfaces

Andreas-Stephan Elsenhans, Michael Stoll

Let $F \in Z [x_{0}, \dots, x_{n}]$ be homogeneous of degree $d$ and assume that $F$ is not a `nullform', i.e., there is an invariant $I$ of forms of degree $d$ in $n + 1$ varia…

math.NT2021

Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces

Timo Keller, Michael Stoll

Let $X$ be one of the $28$ Atkin-Lehner quotients of a curve $X_{0} (N)$ such that $X$ has genus $2$ and its Jacobian variety $J$ is absolutely simple. We show that the Shafarevich-Ta…

math.NT2021★ 1 cited

Elliptic curves with a point of order 13 defined over cyclic cubic fields

Peter Bruin, Maarten Derickx, Michael Stoll

We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $Q$ with a $K$ -rational point of order 13 and such that $E$ is no…