2010 Fiscal Year Final Research Report
Arithmetic geometric approach for period integrals
| Project/Area Number |
20540010
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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 | The University of Tokyo |
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Principal Investigator |
TERASOMA Tomohide The University of Tokyo, 大学院・数理科学研究科, 教授 (50192654)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 周期積分 / モチーフ / 代数的サイクル / ホッジ構造 |
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| Research Abstract |
We study period integrals of algebraic varieties from the view point of algebraic correspondence, algebraic cycles and special functions such as automorphic functions. By applying the method of bar construction to algebraic varieties over positive characteristic base field, we describe their p-fundamental group, and establish a basic tools for Hodge realization functors using Deligne differential graded algebras. We also prove some part of Beilinson conjectures concerning mixed elliptic motives. Concerning automorphic functions, we stablish several new Thomae type theorems related to K3 surfaces, etc.
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