Dirichlet $L$-series at $s = 0$ and the scarcity of Euler systems

Dominik Bullach (King’s College London)

12-May-2022, 09:45-10:45 (23 months ago)

Abstract: In 1989 Coleman made a distribution-theoretic conjecture which predicts that every Euler system `for $\Q$' should essentially be cyclotomic in nature. In this talk I will discuss work joint with Burns, Daoud and Seo which not only allows us to prove Coleman's Conjecture but also provides an elementary interpretation of, and thereby more direct strategy to proving, the equivariant Tamagawa Number Conjecture (eTNC) for Dirichlet $L$-series at $s = 0$. As a concrete application we obtain an unconditional proof of the `minus part' of the eTNC over finite abelian CM extensions of totally real fields.

algebraic geometrynumber theory

Audience: researchers in the topic


Number Theory Seminars at UniversitĂ  degli Studi di Padova

Organizers: Luca Dall'Ava*, Matteo Longo
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