Nickel, Andreas

Annihilating Wild Kernels

Doc. Math. 24, 2381-2422 (2019)
DOI: 10.25537/dm.2019v24.2381-2422
Communicated by Otmar Venjakob

Summary

Let \(L/K\) be a finite Galois extension of number fields with Galois group \(G\). Let \(p\) be an odd prime and \(r>1\) be an integer. Assuming a conjecture of Schneider, we formulate a conjecture that relates special values of equivariant Artin \(L\)-series at \(s=r\) to the compact support cohomology of the étale \(p\)-adic sheaf \(\mathbb{Z}_p(r)\). We show that our conjecture is essentially equivalent to the \(p\)-part of the equivariant Tamagawa number conjecture for the pair \((h^0(\text{Spec}(L))(r),\mathbb{Z}[G])\). We derive from this explicit constraints on the Galois module structure of Banaszak's \(p\)-adic wild kernels.

Mathematics Subject Classification

11R42, 19F27, 11R70

Keywords/Phrases

\(K\)-theory, wild kernels, equivariant Tamagawa number conjecture, special \(L\)-values, Schneider's conjecture, annihilation

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Affiliation

Nickel, Andreas
Universität Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann-Str. 9, 45127 Essen, Germany

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