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

技术描述：该项目为俄克拉何马大学的Brent Gordon提供部分支持，作为客座科学家在孟买的塔塔基础研究所（TIFR）、数学学院和印度阿拉哈巴德的Mehta研究所工作四个月。他的研究领域是算术代数几何。研究的具体问题集中在与自同构形式相关的代数几何变量中的代数循环问题。研究的一个目标是确定霍奇结构，并验证霍奇猜想，为这些品种的特殊成分。第二个目标是分析和理解一些Kuga-Shimura变的代数循环模有理等价群。范围：这个项目将对Gordon教授的研究非常有益，因为它提供了与一些杰出的印度理论家长期的重要联系，他与这些理论家在会议和电子邮件中有有限的联系。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要的互动，这些小组有共同的兴趣，并期望在必要的孵化时间后，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。项目符合INT指导方针，支持有利于美国科学家的新活动。＊＊＊

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. ***