中科院数学与系统科学研究院
数学研究所
数论研讨班
报告人： Yiwen Zhou (周意闻)（University of Chicago）
题 目：Completed cohomology and Kato's Euler system for modular forms
时 间：2018.08.17（星期五），10:00-11:30
地 点：数学院南楼N818室
摘 要：Let f be a cuspidal Hecke eigenform of weight k ≥ 2, V_f the p-adic Galois representation attached to f. Using works of Colmez and Emerton on p-adic local Langlands and local-global compatibility, we can construct an element z_M (M stands for modular symbols) in the local Iwasawa cohomology of V_f^*. In this talk, I will show that the images of z_M under various dual exponential maps computes the classical L-values of the modular form f and its twists. We will then compare z_M with z_Kato - the image of Kato's Euler system in the local Iwasawa cohomology.