2000 Fiscal Year Final Research Report Summary
Arithmetic properties of p-adic and π-adic L-functions
| Project/Area Number |
09640052
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | HOKKAIDO UNIVERSITY (1998-2000)
Tokyo Metropolitan University (1997) |
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Principal Investigator |
TAGUCHI Yuichiro Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (90231399)
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| Co-Investigator(Kenkyū-buntansha) |
KITAGAWA Koji Hokkaido Univ., Grad.School of Sci., Instructor, 大学院・理学研究科, 助手 (70241297)
MAEDA Yoshitaka Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (60173720)
MIYAKE Toshitsune Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (20025430)
SATOH Takakazu Saitama Univ., Fac.of Nat.Sci., Assoc.Prof., 理学部, 助教授 (70215797)
KURIHARA Masato Tokyo Metropolitan Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (40211221)
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| Project Period (FY) |
1997 – 2000
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| Keywords | p-adic representations / Fontaine-Mazur conjecture / finiteness / formal group / Dieudonne module / Frobenius |
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| Research Abstract |
(1) I proved the Finiteness conjecture of Fontaine-Mazur on geometric representations in the potentially abelian case. A similar fact had been proved by Anderson-Blasius-Coleman-Zettler. Their theorem was on compatible systems of l-adic representations, whereas my theorem is on p-adic representations (on one prime p).
(2) Jointly with Prof.T.Satoh, we established a fast algorithm for computing the trace of the Frobenius on the Dieudonne modules of ordinary formal groups over a finite field.
(3) Jointly with H.Moon, we obtained some partial results on mod 7 semisimple Galois representations. According to a conjecture of Serre, there exists no odd and irreducible mod 7 Galois representations unramified outside 7. On the other hand, there is no known precise conjecture on even representations. Here, we proved the nonexistence of even irreducible mod 7 Galois representations unramified outside 7.
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