Let be a line bundle on a scheme , proper over a field. The property of being nef can sometimes be “thickened”, allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line bundle may be nef, but not arithmetically nef. We show that is arithmetically nef if and only if its restriction to its stable base locus is arithmetically nef. Consequently, if is nef and its stable base locus has dimension or less, then is arithmetically nef.
"Arithmetically Nef Line Bundles." Michigan Math. J. 69 (3) 545 - 558, August 2020. https://doi.org/10.1307/mmj/1596700818