Iwasawa theory of Harse zeta functions

关于岩泽的模形式理论，我完成了预印本“p-adic Hoclge理论和模形式zeta函数的值”（244页）。本文证明了关于模形式的岩泽主猜想的一半。(Half在猜想中的意思是一个[小于或等于]，它具有等式“zeta side”=“算术群side”的形式。作为应用，我得到了有理数域上椭圆曲线上BSD簇的结果，关于整体Poeetre特征域上交换簇的BSD“cong”，在Take-Shaturevich群（F. Trihen），与斋藤武共同证明了Blocn的导体公式，这也与Harse zeta函数有关，用对数几何的方法得到了log Hodge理论和log Abel簇的结果。

Concerning Iwasawa theory of moduar forms, I completed the preprint "p-adic Hoclge theory and values of zeta funcions of moduar forms" (244 pages). In this paper, I proved the half of Iwasawa main conjecture for modular forms. (Half means one 【less than or equal】 in the conjecture which has the form of the equality "zeta side"="arithmetic group side.)As an application I obtained results on BSD confectures on elliptic curves over rational number field.Concerning BSD 'cong' for abelian varieties over global fields of poeetre characteristic, I proved it assuming the fimteness of Take-Shaturevich group (with F. Trihen).I proved Blocn's conductor formula by the joint work with Takeshi Saito, This is related also to Harse zeta functions.I obtained results on log Hodge theory and on log abelian varieties by using the method of log geometry.