  In this paper, we show the global well-posedness for periodic gKdV equations
in the space $H^s(\mathbb{T})$, $s\ge \frac12$ for quartic case, and $s>
\frac59$ for quintic case. These improve the previous results of I-team in
2004. In particular, the result is sharp for quintic case. The main approaches
are the I-method combining with the resonance decomposition developed by Miao
et al in 2010, and a bilinear Strichartz estimate in periodic setting.
