Algebraic Cycles in Kuga-Shimura Varieties, Award in Indian Rupees

INT 9406779 Gordon技术描述：该项目为俄克拉荷马大学的Brent Gordon提供部分支持，让他在孟买数学学院塔塔基础研究所担任四个月的客座科学家，并在印度阿拉哈巴德的梅塔研究所担任两个月的客座科学家。他的研究领域是算术代数几何。要研究的具体问题集中在与自同构形式相关的代数几何簇中的代数圈问题上。研究的目标之一是确定Hodge结构，并验证Hodge猜想，为这些品种的特殊成分。第二个目标是分析和理解某些Kuga-Shimura变种的模有理等价的代数圈群。范围：这个项目将对戈登教授的研究非常有益，因为它在很长一段时间内提供了与一些杰出的印度理论家的重要联系，而他在会议和电子邮件中与这些人的联系有限。他预计将与TIFR的两个小组和新梅塔研究所的一个小组进行重大互动，这些小组有共同的兴趣，并预计在必要的孵化时间之后，将制定具体的合作计划。印度科学家擅长理论数学，这种互动可能会带来许多互惠互利。该项目符合INT指导方针，支持一项使美国科学家受益的新活动。***

INT 9406779 Gordon Technical Description: This project provides partial support for Brent Gordon, University of Oklahoma to be a guest scientist for four months at the Tata Institute for Fundamental Research (TIFR), School of Mathematics, Bombay and two months at the Mehta Research Institute, Allahabad, India. His research area is arithmetic algebraic geometry. The specific problems to be investigated focus on questions about algebraic cycles in algebraic-geometric varieties associated with automorphic forms. One goal of the research is to determine the Hodge structure, and verify the Hodge conjecture, for particular special constituents of these varieties. A second goal is to analyze and understand the groups of algebraic cycles modulo rational equivalence for some Kuga-Shimura varieties. Scope: This project will be very beneficial to Prof. Gordon's research by providing vital contact for an extended period with some exceptional Indian theorists with whom he has had limited contact at meetings and via e-mail. He anticipates significant interaction with two groups at TIFR and one group at the new Mehta Research Institute having common interests and expects that after the necessary incubation time specific plans for collaborations will develop. Indian scientists excel in theoretical mathematics and many mutual benefits may be expected to result from the interaction. Project corresponds with INT guidelines by supporting a new activity that benefits a U.S. scientist. ***