| 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)
原田 雅名 京都大学, 大学院・理学研究科, 助教 (80181022)
深谷 太香子 慶應義塾大学, 商学部, 講師 (20365464)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥13,960,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥960,000)
Fiscal Year 2007: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2006: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2005: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2004: ¥3,400,000 (Direct Cost: ¥3,400,000)
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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 / Hodge構造 / 退化 / P進Hodge構造 / ゼータ関数 / regnlator / height pairing / 非可損岩澤理論 / 総実代数体 / 保型形式 / 主予想 / アーベル多様体 / セルマー群 / ルート数 / ガロワ拡大 / 楕円曲線 / $p$進ゼータ関数 / 普遍ノルム / 単数基準 / 非可換 / P進 / L関数 / K_1 |
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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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