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Let
When
The purpose of this note is to investigate various cohomologies of
This paper is meant to be a part of the general program of studying cohomologies with degenerating coefficients on quasiprojective varieties and their Kählerian generalizations. The general aim here is not restricted to the case of curves nor to the one of representations that are unipotent near the divisor. The purpose of this note therefore is to illuminate at this particular case where many of the (analytic and geometric) difficulties of the general case are not present what differences will appear when we consider unipotent harmonic bundles instead of VHSs; for the case of VHSs, the various cohomologies have been considered by various authors [1, 10, 14, 9] and are well understood by now.