In a paper I need to make reference to two conjectures by Gabber, from

* Ofer Gabber, _On purity for the Brauer group_, in: _Arithmetic Algebraic Geometry_, MFO Report No. 37/2004, doi:[10.14760/OWR-2004-37](https://doi.org/10.14760/OWR-2004-37)

(see Conjectures 2 and 3, page 1975)

1) Let $R$ be a strictly henselian complete intersection noetherian 
local ring of dimension at least 4. Then $Br'(U_R) = 0$ (the cohomological Brauer group of the punctured spectrum is $0$).

2) Let $R$ be a complete intersection noetherian local ring of dimension 3. Then $Pic(U_R)$ is torsion-free.  

Does anyone know of any new developments on these conjectures beyond the Oberwolfach report above? I tried MathScinet but could not find anything. May be someone in the  Arithmetic Geometry community happen to know some news on these? Thanks a bunch.