# Motives of isogenous K3 surfaces

## TL;DR

This paper proves that isogenous K3 surfaces share the same Chow motives, offering a new algebraic proof of a longstanding conjecture and deepening the understanding of their motivic properties.

## Contribution

It provides a purely algebraic proof that isogenous K3 surfaces have isomorphic Chow motives, bypassing complex analytic methods used previously.

## Key findings

- Isogenous K3 surfaces have isomorphic Chow motives.
- A new algebraic proof of Safarevich's conjecture is developed.
- The approach avoids twistor spaces and non-algebraic K3 surfaces.

## Abstract

We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevich which has been settled only recently by Buskin. The main step consists of a new proof of Safarevich's conjecture that circumvents the analytic parts in Buskin's approach, avoiding twistor spaces and non-algebraic K3 surfaces.