Annihilating Wild Kernels

  • Andreas Nickel

    Universität Duisburg-Essen, Fakultät für Mathematik, Thea-Leymann-Str. 9, 45127 Essen, Germany
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Let L/KL/K be a finite Galois extension of number fields with Galois group GG. Let pp be an odd prime and r>1r>1 be an integer. Assuming a conjecture of Schneider, we formulate a conjecture that relates special values of equivariant Artin LL-series at s=rs=r to the compact support cohomology of the étale pp-adic sheaf Zp(r)\mathbb{Z}_p(r). We show that our conjecture is essentially equivalent to the pp-part of the equivariant Tamagawa number conjecture for the pair (h0(Spec(L))(r),Z[G])(h^0(\text{Spec}(L))(r),\mathbb{Z}[G]). We derive from this explicit constraints on the Galois module structure of Banaszak's pp-adic wild kernels.

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Andreas Nickel, Annihilating Wild Kernels. Doc. Math. 24 (2019), pp. 2381–2422

DOI 10.4171/DM/728