[SNU Number Theory Seminar 2022-06-03] The Coleman conjecture on circular distributions and the equivariant Tamagawa Number conjecture

by qsms posted May 18, 2022
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일정시작 2022-06-03
배경색상 #FF5733
  • Date :  2022-06-3  (Fri) 16:00

  • Place :  27-325 (SNU)

  • Speaker :  Soogil Seo (Yonsei University)
  • Title :  The Coleman conjecture on circular distributions and the equivariant Tamagawa Number conjecture
  • Abstract :  

    We introduce the Coleman conjecture on circular distributions made around 1980's and its implications in Euler systems over Q. In our joint work with Burns, Bullach and Daoud, we will provide a proof of the Coleman conjecture and introduce "Coleman's conjecture for higher ranks" with its application to the equivariant Tamagawa Number conjecture for Dirichlet L-functions at s=0 (eTNC (G_m), in short) of Bloch, Kato, Burns and Flach. Based on the method used in the proof of Coleman's conjecture, we provide a proof of the minus part of eTNC(G_m) for CM extensions of totally real fields unconditionally and imaginary quadratic fields under mu vanishing condition, which accordingly recovers or implies refinements and variants of ‘Stark-type conjectures’ (in particular, conjectures of Rubin-Stark, Brumer, Chinberg, and the lifted root number conjecture of Gruenberg, Rittel and Weiss, among others).

  • Website:  https://sites.google.com/view/snunt/seminars

 

 

 

 


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