| Project/Area Number |
14340013
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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 | HIROSHIMA UNIVERSITY |
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Principal Investigator |
TSUZUKI Nobuo Hiroshima University, Gaduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (10253048)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Hiroyuki Hiroshima University, Graduate School of Engineering, Associate Professor, 大学院・工学研究科, 助教授 (60232469)
KATO Fumiharu Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50294880)
KIMARA Shun-ichi Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (10284150)
SUGIYAMA Kenichi Chiba University, Faculty of Science, Associate Professor, 理学部, 助教授 (90206441)
TAGUCHI Yuichiro Kyusyu Univerity, Faculty of Mathematics, Associate Professor, 大学院・数理学研究院, 助教授 (90231399)
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| Project Period (FY) |
2002 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥10,600,000 (Direct Cost: ¥10,600,000)
Fiscal Year 2004: ¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2003: ¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 2002: ¥3,700,000 (Direct Cost: ¥3,700,000)
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| Keywords | tubular neighborhoods / cohomological descent / hypercoverings / rigid analytic spaces / rigid cohomology / p-adic representations / de Rham cohomology / motives / 単体的多様体 / 被覆と細分 / 過収束アイソクリスタル / 純性定理 / Zariski-永田の定理 / ドラムコホモロジー / リジッドコホモロジー / 比較写像 / 埋め込み系 / 計算アルゴリズム / オーバーコンバージェントアイソクリスタル / コホモロジー的降下理論 / 固有超被覆 / p進解析 / 国際研究者交流 / オランダ:イタリア |
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| Research Abstract |
The head investigator studied the cohomology theories for varieties of positive characteristic under the key words : tubular neighborhoods and cohomological descent. The contents are as follow ; (1)Construction of tubular neighborhoods of simplicial varieties, (2)Cohomological descent in rigid cohomology (partially collaborated with Chiarellotto), (3)Generic finiteness of relative rigid cohomology for proper and smooth morphisms, (4)Cohomological descent in de Rham cohomology and Hodge filtrations (collaborated with Chiarellotto), (5)Comparison map between rigid and de Rham cohomologies for simplicial families, and (6)Purity theorem for overconvergent isocrystals.
Kato studied (1)Mumford curves and p-adic orbifolds with a covering which are Mumford curves (collaborated with Cornelissen), and (2)the foundations of rigid analytic spaces (collaborated with Fujiwara). Kimura studied the finite dimensionality of motives. Ito worked on algorithms of computing numbers of rational points of varieties over finite fields with the head investigator. Sugiyama studied (1)the BSD type problem in the Selberg Zeta functions for 3-dimentional manifolds and (2)a geometric analogue of Langlands correspondence. Shiho developed (1)the theory of crystalline fundamental group and (2)the theory of weights using logarithmic crystalline cohomology. Sumida studied several Iwasawa invariants for number fields. Taguchi had results on the finiteness of Galois representations with certain conditions (collaborated with Moon),. He also worked on the fast algorithm for computing numbers of rational points of elliptic curves over finite fields (collaborated with Sato),.
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