ICTS:31802

Video URL

Lectures on the Anticyclotomic main conjecture-I

Lectures on the Anticyclotomic main conjecture-I

(2025). Lectures on the Anticyclotomic main conjecture-I. SciVideos. https://youtube.com/live/EvwQqgpCmCo

Lectures on the Anticyclotomic main conjecture-I. SciVideos, May. 21, 2025, https://youtube.com/live/EvwQqgpCmCo 

          @misc{ scivideos_ICTS:31802,
            doi = {},
            url = {https://youtube.com/live/EvwQqgpCmCo},
            author = {},
            keywords = {},
            language = {en},
            title = {Lectures on the Anticyclotomic main conjecture-I},
            publisher = {},
            year = {2025},
            month = {may},
            note = {ICTS:31802 see, \url{https://scivideos.org/icts-tifr/31802}}
          }
Haruzo Hida
Talk numberICTS:31802
Source RepositoryICTS-TIFR

Abstract

We first prove, for a prime p>3 unramified in a CM quadratic extension of a totally real field F, h(M/F)L(\chi)|H(\psi)|h(M/F)F(\chi) (h(M/F)=h(M)/h(F)) in \Lambda for the congruence power serie H(\psi) of \psi lifting a fixed anti-cyclotomic character \chi and anticyclotomic Katz p-adic L-function L(\chi) of branch character \chi, built on the lectures by Tilouine proving this over \Lambda[1/p]. Here \Lambda is the many variable Iwasawa algebra of M. In the second lecture, we give a sketch of the proof of the reverse divisibility: H(\psi)|h(M/F)L(\chi) resulting in the main conjecture, as H(\psi)=h(M/F)F(\chi) for the anticyclotomic Iwasawa power series F(\chi) by the “R=T”-theorem.