UNIVERSAL DEFORMATION SPACE OF P-DIVISIBLE SMOOTH FORMAL GROUPS OVER Fp

for understanding me most thoroughly and supporting me most firmly in the world ii Acknowledgments Foremost, I would like to express my sincere gratitude to my advisor Professor Ching-Li Chai for his continuous support to my Ph.D. study and research. This thesis work would not have been written without his patience, encouragement, enthusiasm, immense knowledge, and numerous hours spent on discussion with me. I could not have imagined having a better advisor for my Ph.D. study. Besides my advisor, I would like to thank the faculty at the University of Penn-sylvania, especially Steven S. Shatz, Ted Chinburg, Florian Pop, David Harbater, and Tony Pantev, for what they taught me during the past five years. I would also like to thank Professor Frans Oort for his questions and encouragement during his visits to the University of Pennsylvania. I would like to thank Janet Burns, Monica Pallanti, and Paula Scarborough for making the department like a family to me. I am grateful to my fellow graduate students Zhaoting Wei, Ying Zhang, Hilaf Hasson, Ryan Eberhart, and Adam Topaz for their help in mathematics and oth-erwise. My life would not have been much fun without the pleasant memories on movies with Shanshan Ding and Paul Levande, chats with Edvard Fagerholm, and iii many other activities with Haomin Wen and Tong Li. Final thanks go to my parents, Weidong Jing and Chunling Zhang, for their love, and Fang Liu, for new delight in my life. i