On a conjecture of Zhao related to standard relations among cyclotomic multiple zeta values

TL;DR

This paper proves Zhao's conjecture on relations among cyclotomic multiple zeta values in weight two, establishing an algebraic framework and equivalence between schemes related to finite abelian groups.

Contribution

It provides a proof of Zhao's conjecture and formulates a broader algebraic setting linking schemes associated with finite abelian groups.

Findings

Proof of Zhao's conjecture in weight two

Establishment of an algebraic equivalence between schemes

Broader algebraic framework for relations among cyclotomic multiple zeta values

Abstract

We provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence between two schemes attached to a finite abelian group $G$. In particular, when $G$ is the group of roots of unity, these schemes describe the standard relations among cyclotomic multiple zeta values.