Non-commutative I wa sawa theory

点击翻译按钮获取中文摘要

With J.Coaten, T. Fukaya, R. Sujatha, and O. Verjakob, the head investigator K. Kato formulated "main conjecture" of non-commutatire Iwasawa theory. K. Kato obtained progresses in attacking this main conjecture. The key approach started by him is the study of K_1 of non-commutatire Iwasawa algebras. This opened the way to reduce non-commutatire Iwasawa theory, to Commutatire Iwasawa theory and congruences between various commutatire p-adic zeta functions. In the case the Galois group is of Heisenberg type, K.Kato proved the main conjecture in the non-commutatire Iwasawa theory of non-commutatire Iwasawa theory of totally real fields.With S. Usui and C. Nakayama, K. kato studied degeneration of mixed Hodge structure, and obtained the mixed Hodge version of SL(2)-orbit thesrem. He obtained the p-adic version with. S. Bloch, K, kato obtained results on the behavior of regulator in degeneration and showed that zeta values appear there. This is a hew direction of Iwasawa theory.