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This paper studies semi-supervised video object segmentation through boosting intra-frame interaction. Recent memory network-based methods focus on exploiting inter-frame temporal reference while paying little attention to intra-frame spatial dependency. Specifically, these segmentation model tends to be susceptible to interference from unrelated nontarget objects in a certain frame. To this end, we propose Global Spectral Filter Memory network (GSFM), which improves intra-frame interaction through learning long-term spatial dependencies in the spectral domain. The key components of GSFM is 2D (inverse) discrete Fourier transform for spatial information mixing. Besides, we empirically find low frequency feature should be enhanced in encoder (backbone) while high frequency for decoder (segmentation head). We attribute this to semantic information extracting role for encoder and fine-grained details highlighting role for decoder. Thus, Low (High) Frequency Module is proposed to fit this circumstance. Extensive experiments on the popular DAVIS and YouTube-VOS benchmarks demonstrate that GSFM noticeably outperforms the baseline method and achieves state-of-the-art performance. Besides, extensive analysis shows that the proposed modules are reasonable and of great generalization ability. Our source code is available at https://github.com/workforai/GSFM.