Non-commutative I wa sawa theory

与J.Coaten，T.福谷河Sujatha和O. Verjakob，首席调查员K。加藤提出了非对易岩泽理论的“主要猜想”。K. Kato在对这一主要猜想的攻击中取得了进展。他开创的关键方法是研究非交换岩泽代数的K_1。这开辟了道路，以减少非commutatire岩泽理论，以Commutatire岩泽理论和各种commutatire p进zeta函数之间的同余关系。K.Kato在Galois群为Heisenberg型的情况下证明了全真实的域的非对易岩泽理论中的主要猜想。和C. Nakayama，K. kato研究了混合Hodge结构的退化，得到了SL（2）-轨道的混合Hodge形式.他得到了p-adic版本。S. Bloch、K、kato获得了有关变性中调节剂行为的结果，并表明zeta值出现在那里。这是岩泽理论的一个新方向。

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.