B. Bekker

activity

20172026

most citedThe divisibility by 2 of rational points on elliptic curves

4 citations · 5 across the 5 of their papers we have counts for

collaborators

7 papers

math.NT2026

Torsion points of small order on cyclic covers of $P^{1}$ . III

Boris M. Bekker, Yuri G. Zarhin

Let $d > 1$ be an integer and $K_{0}$ a perfect field such that $c ha r (K_{0})$ does not divide $d$ . Let $n > d$ be an integer that is prime to $d$ . Let $f (x) \in K_{0} [x]$ be a degree $n$ moni…

math.AG2025

Torsion points of small order on cyclic covers of $P^{1}$ . II

Boris Bekker, Yuri G. Zarhin

Let $d \geq 2$ be an integer, $K_{0}$ a perfect field such that $c ha r (K_{0})$ does not divide $d$ , $n > d$ an integer prime to $d$ , $f (x) \in K_{0} [x]$ a degree $n$ monic polynomial withou…

math.AG2024

Torsion points of small order on cyclic covers of $P^{1}$

Boris M. Bekker, Yuri G. Zarhin

Let $d \geq 2$ be a positive integer, $K$ an algebraically closed field of characteristic not dividing $d$ , $n \geq d + 1$ a positive integer that is prime to $d$ , $f (x) \in K [x]$ a deg…

math.AG2021

Torsion points of small order on hyperelliptic curves

Boris M. Bekker, Yuri G. Zarhin

Let $C$ be a hyperelliptic curve of genus $g > 1$ over an algebraically closed field $K$ of characteristic zero and $O$ one of the $(2 g + 2)$ Weierstrass points in $C (K)$ . Let $J$ be t…

math.AG2019★ 1 cited

Torsion Points of order 2g+1 on odd degree hyperelliptic curves of genus g

Boris M. Bekker, Yuri G. Zarhin

Let $K$ be an algebraically closed field of characteristic different from $2$ , $g$ a positive integer, $f (x) \in K [x]$ a degree $2 g + 1$ monic polynomial without repeated roots, $C_f:…

math.AG2017

Families of elliptic curves with rational torsion points of even order

Boris M. Bekker, Yuri G. Zarhin

This paper is a follow up of arXiv:1702.02255 [math.NT]. We construct explicitly versal families of elliptic curves with rational points of order 4, 6, 8, 10, 12 respectively.

math.NT2017★ 4 cited

The divisibility by 2 of rational points on elliptic curves

Boris M. Bekker, Yuri G. Zarhin

We give a simple proof of the well-known divisibility by 2 condition for rational points on elliptic curves with rational 2-torsion. As an application of the explicit division by $…

Torsion points of small order on cyclic covers of P1. III

Torsion points of small order on cyclic covers of P1. II

Torsion points of small order on cyclic covers of P1

Torsion points of small order on hyperelliptic curves

Torsion Points of order 2g+1 on odd degree hyperelliptic curves of genus g

Families of elliptic curves with rational torsion points of even order

The divisibility by 2 of rational points on elliptic curves

Torsion points of small order on cyclic covers of $P^{1}$ . III

Torsion points of small order on cyclic covers of $P^{1}$ . II

Torsion points of small order on cyclic covers of $P^{1}$