This paper deals with the cohomology of infinitesimal quantum general linear groups. We prove that Hood ((Gq)1, K.) 0 and Hev ((Gq)1, K) KN. Our ap-proach is to consider the q-analogue of a unipotent group scheme and construct a filtration of the Hochschild complex for K (Uq) 1. Meanwhile a certain q-deforma-tion of a polynomial coalgebra arises naturally, which is also believed to be interesting.