Anticyclotomic Iwasawa theory for Hilbert modular forms

Open Access
Author:
Wang, Haining
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
None
Committee Members:
  • Winnie Li, Dissertation Advisor
  • Winnie Li, Committee Chair
  • Yuriy G Zarkhin, Committee Member
  • Dale Brownawell, Committee Member
  • Emily Rolfe Grosholz, Committee Member
  • Ming Lun Hsieh, Special Member
Keywords:
  • Iwasawa theory
  • Hilbert modular forms
Abstract:
In this dissertation, we study the Iwasawa theory for Hilbert modular forms over the anticyclotomic extension of a CM field. We prove a one sided divisibility result toward the Iwasawa main conjecture. The proof relies on the first and second reciprocity law relating theta elements to Heegner points Euler system. As a by-product we also prove certain Bloch-Kato type result in the rank 0 case and a parity conjecture.