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

Showing math.NTShow all

42 papers · 1 filter

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…

math.NT2019★ 1 cited

An application of "Selmer group Chabauty" to arithmetic dynamics

Michael Stoll

We describe how one can use the "Selmer group Chabauty" method developed by the author to show that certain hyperelliptic curves of the form $C : y^{2} = x^{N} + h (x)^{2},$ w…