
Date : 20220603 (Fri) 16:00

Place : 27325 (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 Lfunctions 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 ‘Starktype conjectures’ (in particular, conjectures of RubinStark, Brumer, Chinberg, and the lifted root number conjecture of Gruenberg, Rittel and Weiss, among others).
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