  We prove that the absolute integral closure $R^{+}$ of an equicharacteristic
zero noetherian complete local domain $R$ is not coherent, provided
$\dim(R)\geq 2$. As a corollary, we give an elementary proof of the mixed
characteristic version of the result due to Asgharzadeh and extend it to
dimension $3$. Furthermore, we apply the methods of Aberbach and Hochster used
to prove the positive characteristic version of this result to study F-coherent
rings and our work naturally suggests a mixed characteristic analogue of a
result of Smith.
