Period domains and related studies in arithmetic

建议者K。Kato与C. Nakayama和S.我是阿吉这推广了经典的厄米对称域的环面紧化理论。他还获得了p-adic模拟它。这些作品的周期域有关的许多有趣的领域。调节器映射和局部高度配对的渐近行为，动机的退化，物理学中出现的发散的渐近行为，霍奇猜想，以及岩泽理论。与岩泽理论的关系来自于调节器映射和zeta值相关的事实，也来自于模簇的紧化的边界在沙里菲图的推广中起着重要作用，沙里菲图对岩泽主要猜想进行了改进。退化的研究也与方案的分歧理论有关。提议者希望研究这些领域。在沙里菲理论的推广中，他与联合首席研究员T。福谷.这项研究提供了新的霍奇理论，算术和物理之间的相互作用。 不同领域的人可以通过这项研究进入其他领域。提案人预计，许多研究生将选择在与本提案中的材料相关的领域撰写论文。

The proposer K. Kato constructed moduli spaces of degenerating mixed Hodge structures in joint works with C. Nakayama and S. Usui. This extends the classical theory of toroidal compactifications of Hermitian symmetric domains. He also obtained the p-adic analogue of it. These works on period domains are related to many interesting areas. Asymptotic behaviors of regulator maps and local height pairings, degeneration of motives, asymptotic behaviors of divergences which occur in physics, Hodge conjecture, and also to Iwasawa theory. The relation to Iwasawa theory comes from the fact that the regulator maps and zeta values are related, and also comes from the fact that the boundary of the compactifications of modular varieties play important roles in the generalization of Sharifi conjectures which give refinements of Iwasawa main conjecture. The study of degeneration is also related to ramification theory of schemes. The proposer wishes to study these areas. In the generalization of Sharifi conjectures, he collaborates with the co-principal investigator T. Fukaya.This study provides new interactions between Hodge theory, arithmeticand physics. People in different areas can enter the other fields via this study. The proposer anticipates that many graduate students will choose to write theses in areas related to the materials in this proposal.