In a paper I need to make reference to 2 conjectures by Gabber

(see Conjectures 2 and 3, page 1975)

http://www.mfo.de/programme/schedule/2004/32/OWR_2004_37.pdf

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.