2007 Fiscal Year Final Research Report Summary
Non-commutative I wa sawa theory
| Project/Area Number |
16340005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
KATO Kazuya Kyoto University, Graduate school of sci, Professor (90111450)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Hiroyuki Kyoto Univ, Graduate school of sci, Professor (40108973)
IKEDA Tamotsu Kyoto Univ, Graduate school of sci, Professor (20211716)
UENO Kenji Kyoto Univ, Graduate school of sci, Professor (40011655)
KATO Fumiharu Kyoto Univ, Graduate school of sci, Associate Professor (50294880)
HIRAGA Iku Kyoto Univ, Graduate school of sci, Lecturer (10260605)
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| Project Period (FY) |
2004 – 2007
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| Keywords | Non-commutafice Iwasawa theroy / Iwasawa theroy / Iwasawa algebra / K_1-group / P-adic veta function / Hodge structure / reglator / Galois group |
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| Research Abstract |
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.
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