Y. Zarhin

activity

20242026

collaborators

10 papers

math.AG2026

Prym varieties that are not isomorphic to Jacobian

Yuri G. Zarhin

We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order $p > 2$ . Using…

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.AG2025

Jacobians with with automorphisms of prime order

Yuri G. Zarhin

In this paper we study principally polarized abelian varieties that admit an automorphism of prime order $p > 2$ . It turns out that certain natural conditions on the multiplicities o…

math.NT2025

Odd and Even Elliptic Curves with Complex Multiplication

Yuri G. Zarhin

We call an order $O$ in a quadratic field $K$ odd (resp. even) if its discriminant is an odd (resp. even) integer. We call an elliptic curve $E$ over the field $C$ of complex numbe…

math.AG2025

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…

Prym varieties that are not isomorphic to Jacobian

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

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

Jacobians with with automorphisms of prime order

Odd and Even Elliptic Curves with Complex Multiplication

Torsion points of small order on cyclic covers of P1

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 $P^{1}$