Geller's conjecture on injectivity of $K_2$ for one-dimensional local domains

Let $A$ be a local one-dimensional domain with field of fractions $F$. Geller's conjecture. The ring $A$ is regular if and only if the map

$$K_2(A)\longrightarrow K_2(F)$$

is injective.

The conjecture gives a criterion for regularity in terms of the injectivity of the map from the second algebraic K-group of a singular or regular local ring to that of its fraction field. It was verified in several cases, including noetherian equicharacteristic characteristic-zero rings that are seminormal with finite normalisation and cuspidal rings of the form $K[t^2,t^3]$, but remains unknown in almost all other cases.