2013 Fiscal Year Final Research Report
A study of arithemetic geometry by p-aidc methods
| Project/Area Number |
22340001
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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 | Tohoku University |
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Principal Investigator |
TSUZUKI NOBUO 東北大学, 理学(系)研究科(研究院), 教授 (10253048)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Fumiharu 熊本大学, 大学院・理学研究科, 教授 (50294880)
SHIHO Atsushi 東京大学, 大学院・数理科学研究科, 准教授 (30292204)
YAMAZAKI Takao 東北大学, 大学院・理学研究科, 教授 (00312794)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAJIMA Yukiyoshi 東京電機大学, 工学部, 准教授 (80287440)
YAMAUCHI Takuya 鹿児島大学, 教育学部, 准教授 (90432707)
KAWAMURA Hisa-aki 広島大学, 大学院・理学研究科, 助教 (00533746)
ABE Tomoyuki 東京大学, 大学院・数理科学研究科, 特任助教 (70609289)
SUWA Noriyuki 中央大学, 理工学部, 教授 (10196925)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 数論幾何 / 数論的D加群 / リジッド解析幾何 / p進コホモロジー / 過収束Fアイソクリスタル / Clemens-Schmid完全列 / 重みモノドロミースペクトル系列 / 国際研究者交流 |
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| Research Abstract |
We investigated the foundation of p-adic methods in arithmetic geometry, rigid analytic technique and cohomology theory arising from differential forms (i.e., p-adic cohomology), and applied them to study arithmetic varieties. We construct p-adic Clemens-Schmid exact sequence for semistable families over algebraic curves of positive characteristic, which is a p-adic analogue of exact sequence describing kernel and cokernel of monodromy operations for semistable families over the complex unit disk. We studied the purity theorem for isocrystals and established the full faithfulness of restriction functors to open subschemes for isocrystals on geometrically unibranch varieties of positive characteristic. As a consequence, we proved pure of weight 1 for first rigid cohomology of proper and geometrically unibranch varieties. We also developed the weight theory in p-adic cohomology and the theory of arithmetic D-modules.
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