Massey products and elliptic curves

TL;DR

This paper investigates the conditions under which higher-order Massey products vanish in the cohomology of elliptic curves over perfect fields, providing a complete characterization for triple Massey products.

Contribution

It offers a comprehensive analysis of Massey product vanishing for elliptic curves, especially characterizing non-vanishing of triple Massey products, advancing understanding in algebraic geometry and cohomology.

Findings

Complete characterization of when triple Massey products do not vanish for elliptic curves.

Conditions for vanishing of higher-order Massey products in the context of elliptic curves.

Enhanced understanding of the cohomological properties of elliptic curves over perfect fields.

Abstract

We study the vanishing of Massey products of order at least $3$ for absolutely irreducible smooth projective curves over a perfect field with coefficients in $\mathbb{Z}/\ell$. We mainly focus on elliptic curves, for which we obtain a complete characterization of when triple Massey products do not vanish.