In this paper, we study the kernel of the reciprocity map of certain simple normal crossing varieties over a finite field and give an example of a simple normal crossing surface whose reciprocity map is not injective for any finite scalar extension.
"On the Kernel of the Reciprocity Map of Simple Normal Crossing Varieties over Finite Fields." Tokyo J. Math. 35 (2) 513 - 526, December 2012. https://doi.org/10.3836/tjm/1358951336