Period domains and related studies in arithmetic

作者K. Kato与C. Nakayama和S.臼井共同构建了退化混合Hodge结构的模空间。这扩展了厄米对称域的环面紧化的经典理论。他也得到了它的p进模拟。这些关于时期域的研究涉及到许多有趣的领域。调节器映射和局部高度配对的渐近行为，动机的退化，物理中出现的散度的渐近行为，Hodge猜想，以及Iwasawa理论。与Iwasawa理论的关系来自于调节映射和zeta值是相关的，也来自于模变紧化的边界在Sharifi猜想的推广中起着重要的作用，Sharifi猜想给出了Iwasawa主猜想的改进。退化的研究也与方案的分枝理论有关。提议者希望研究这些领域。在Sharifi猜想的概括中，他与联合首席研究员T. Fukaya合作。这项研究提供了霍奇理论、算术和物理之间新的相互作用。不同领域的人可以通过这项研究进入其他领域。申请人预计许多研究生将选择在与本提案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.