The Brauer-relation parity conjecture for Jacobians

Let $X$ be a curve defined over a number field $K$, and let $G$ be a finite group of $K$-automorphisms of $X$. Assume that $\Omega^{1}(\operatorname{Jac}_X)$ is self-dual as a $G$-representation. Let $\Theta$ be a Brauer relation in $G$, let $p$ be a prime, and let $w(X^{\tau_{\Theta,p}}/K_v)$ and $\Lambda_\Theta(X/K_v)$ denote the associated local root number and regulator-constant term. The Brauer-relation parity conjecture.

$$\prod_{v\textup{ place of }K} w(X^{\tau_{\Theta,p}}/K_v) (-1)^{\operatorname{ord}_p \Lambda_\Theta(X/K_v)} = 1.$$

This is the local-term comparison needed to obtain the parity conjecture for the relevant self-dual representation components of the Jacobian. The supplied text does not state that it has been proved or disproved.