Reliable environmental perception is essential for intelligent ships, with three-dimensional (3D) point cloud ship detection providing spatial information for situational awareness and collision avoidance. However, unstable cross-frame geometric correspondence, ambiguous historical associations, and unreliable temporal fusion hinder the use of historical information. We propose GeoST for temporal maritime LiDAR ship detection, using object-local representations as a basis for geometric support-guided historical feature modulation and fusion. Built on FASTer, GeoST normalizes observations within their respective proposal coordinate systems and associates them by object dimensions and shape, constructing temporal inputs without external ego-vessel poses. The multi-scale anisotropic point feature enhancement module (PointMKDA) aggregates neighborhood features across scales and orientations to enhance local geometric representations. The geometrically constrained cross-attention module (GCAM) uses enhanced current-frame focal point features to update historical features and estimate geometric support. The reliability-guided feature modulation (RGFM) module combines this support, association priors, observation age, and learned features to generate modulation weights across temporal, point, and channel dimensions, regulating feature contributions before temporal fusion. GeoST achieved 3D average precision (AP) of 87.17% and 73.09% at intersection-over-union (IoU) thresholds of 0.5 and 0.7, respectively, exceeding FASTer by 2.81 and 2.27 percentage points.