## 1 Introduction  
Agricultural green development is one critical path of China's ecological civilization construction and also the inevitable approach to achieving the target of agricultural carbon peaking and carbon neutrality strategy [1]. However, the current agricultural extensive management mode in China, which mainly relies on resource consumption with high emissions, has not been changed and caused serious problems of agricultural non-point source pollution and ecological degradation [2]. As such, China has issued policies to address agricultural green development. First, an overall layout of ecological, agricultural and other functional spaces is formulated. Second, the environmental pollution bottom line of agricultural green development and environmental protection responsibility target assessment has been strictly executed by the agricultural and rural comprehensive administrative law enforcement team to promote environmental regulation. Third, the funds to support agricultural green development have been increased in recent years. Thus, to realize the fundamental reform of extensive agricultural development mode and promote agricultural green development, both financial support for agriculture and environmental regulation are essential [3]. Current research also shows that financial support for agriculture and environmental regulation are the main measures to promote agricultural green development [4]. On the one hand, financial support for agriculture could promote not only the local level of agricultural green development but also that of other adjacent regions. This is because the local government would provide a series of subsidies and incentives to local agricultural operators for emission reduction and technological innovation [5; 6]. It will promote the generation of new technologies for agricultural green development; accordingly, the level of agricultural green development in adjacent regions would also be promoted with knowledge diffusion and technology spillover [7; 8]. In addition, due to the differences in resource endowments and policies of financial support for agriculture among different areas, the influence mechanism of financial support for agriculture on agricultural green development has shown different spatial effects in different areas [9]. Moreover, the performance appraisal objectives for local governments have varied from gold and silver mountains to clear water and green mountains with the target of carbon peaking and carbon neutrality strategy. As such, local governments have reduced carbon emissions through financial environmental expenditure, which has a demonstration function to their adjacent regions [10; 11; 12]. On the other hand, environmental regulation is also regarded as an important element for promoting agricultural green development [12]. Based on the \"strong porter hypothesis\", reasonable environmental regulation could promote the upgrading of agricultural industrial structure and technical innovation in the local area, reducing agricultural pollution and agricultural carbon emissions. Moreover, due to the spillover characteristics of agricultural pollution, local environmental regulation also retains the transfer of agricultural pollution to adjacent regions and indirectly improves their agricultural environment [13]. However, as the cost-following theory suggested that strict environmental regulation would be higher than the input cost of agricultural development, which could not improve the inefficiency of agriculture, but aggravate both local and adjacent agricultural pollution [9; 14], thus finally inhibiting agricultural green development in both local and adjacent regions. Therefore, this paper explores the relationship between environmental regulation, financial support for agriculture and agricultural green development from a spatial spillover perspective. What are the temporal and spatial evolution characteristics of agricultural green development?