On various generalizations of Iwasawa theory

点击翻译按钮获取中文摘要

We obtained several results on generalized Iwasawa theory especially on the function-field analogue of Iwasawa theory studying abelian varieties over global fields of positive characteristic and the deformation-theoretic generalization of Iwasawa theory. For the algebraic side of Iwasawa theory, we proved the control theorem to study the behavior of Selmer groups on Hida deformations of Hilbert modular forms. For the analytic side of the theory, we constructed the p-adic L-functions in several variables on Hida deformations of Hilbert modular forms. We also worked on the Hida deformations of Siegel modular forms. We constructed the Coleman. Perrin-Riou map which interpolates dual exponential maps on the deformation. We also generalized our result on Euler system for deformation spaces removing the assumption that the deformation ring is regular.