2021/11/29 by Bullach, Dominik, Burns, David, Daoud, Alexandre +1
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2111.14689
We study Euler systems for \mathbbGm over a number field k. Motivated by a distribution-theoretic idea of Coleman, we formulate a conjecture regarding the existence of such systems that is elementary to state and yet strictly finer than Kato's equivariant Tamagawa number conjecture for Dirichlet L-series at s=0. To investigate the conjecture, we develop an abstract theory of `Euler limits' and, in particular, prove the existence of canonical `restriction' and `localisation' sequences in this theory. By using this approach we obtain a variety of new results, ranging from a proof, modulo standard μ-vanishing hypotheses, of our central conjecture in the case k is ℚ or imaginary quadratic to a proof of the `minus part' of Kato's conjecture in the case k is totally real. In proving these results, we also show that higher-rank Euler systems for a wide class of p-adic representations control the structure of Iwasawa-theoretic Selmer groups in the manner predicted by `main conjectures'.