Completed Cohomology and Kato's Euler System for Modular Forms
Time: 2018-09-26
Published By: Meng Yu
Speaker(s): Yiwen Zhou (University of Chicago)
Time: 14:00-16:00 September 27, 2018
Venue: Room 82J04, Jiayibing Building, Jingchunyuan 82, BICMR
Abstract: Let f be a cuspidal Hecke eigenform of weight k ≥ 2, V_f the p-adic Galois representation attached to f. Using Emerton's work on local-global compatibility and Colmez's work on p-adic local Langlands, we can think of the modular symbol {0 - ∞} as an element in
the local Iwasawa cohomology of V_f^*. In this talk, I will show that this element coincides with Kato's Euler system, under the assumption that V_f restricted to G_Qp is absolutely irreducible.
the local Iwasawa cohomology of V_f^*. In this talk, I will show that this element coincides with Kato's Euler system, under the assumption that V_f restricted to G_Qp is absolutely irreducible.