| Co-Investigator(Kenkyū-buntansha) |
志甫 淳 東京大学, 大学院数理科学研究科, 教授 (30292204)
阿部 知行 東京大学, カブリ数物連携宇宙研究機構, 教授 (70609289)
中島 幸喜 東京電機大学, 工学部, 教授 (80287440)
山内 卓也 東北大学, 理学研究科, 准教授 (90432707)
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| Budget Amount *help |
¥40,560,000 (Direct Cost: ¥31,200,000、Indirect Cost: ¥9,360,000)
Fiscal Year 2022: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2021: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2020: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2019: ¥8,840,000 (Direct Cost: ¥6,800,000、Indirect Cost: ¥2,040,000)
Fiscal Year 2018: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
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| Outline of Final Research Achievements |
We have studied slopes of Frobenius operations and their variations, which are important invariants in arithmetic geometry, and established several new achievements. One of the most important results is an affirmative solution of “Minimal slope conjecture” which were proposed by K.Kedlaya. The minimal slope conjecture asserts a huge p-adic representation of fundamental group, which arises from the minimal slope part of irreducible overconvergent F-isocrystals, determines a whole geometric object. The phenomenon should be naturally captured by p-adic methods. In addition, we have obtained a certain constancy of slopes of F-isocrystals on algebraic varieties of positive characteristic and developments of p-adic cohomology theory.
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