Speaker : Mr. Sheng-Chi Shih (University of Arizona)
Title : On congruence modules related to Hilbert Eisenstein series II
Time : 2017-12-22 (Fri) 15:00-16:15
Place : Seminar Room 609, Institute of Mathematics (NTU Campus)
Abstract: The Iwasawa main conjecture asserts a relationship between certain $p$-adic $L$-functions and characteristic polynomials associated with the $p$-part of the class group of the cyclotomic Zp-extension of an abelian.extension of Q. The main conjecture over abelian extensions of Q was first proved by Mazur and Wiles using $2$-dimensional Galois representations attached to cusp forms that are congruent to ordinary Eisenstein series. Wiles generalized the method of Mazur-Wiles to the setting of Hilbert modular forms and proved the main conjecture over totally real fields. A few years later, Ohta gave a refinement of Wiles's proof of the main conjecture over abelian extensions of Q by constructing Galois representations attached to cusp forms using the action of Gal(Qbar/Q) on the cohomology of modular curves. One of the key steps in Ohta's proof is to compute the congruence modules related to Eisenstein series.