  We calculate the Next-to-Leading Order (NLO) virtual correction to the
Higgs-induced DIS coefficient function in the infinite top-mass limit. Since we
want to use this result in the framework of kt-factorization to resum small-x
logarithms up to Next-to-Leading-Logarithm (NLL), we work in light-cone gauge
and we keep the incoming gluon off-shell. This choice raises many challenging
points like the presence of spurious singularities and a different definition
for the UV-counterterms. This calculation is a necessary ingredient for the
coefficient function that will be used to resum up to NLL small-x logarithms
for this process.
