Variation of class groups and Selmer groups in infinite pro-p tower
摘要: In 1959, Iwasawa first derived his celebrated formula which describes the growth of the p-exponents of the class groups in a Zp-extension. A natural direction of study is to consider analogus formulas for other p-adic Lie extensions. Another direction was taken up by Mazur, where he applied Iwasawa's philosphy to study the growth of the Mordell-Weil rank of an abelian variety over a Zp-extension. In this talk, we shall survey some of the research activities revolving around these studies.