Geodesic
Annihilating Wild Kernels
Documenta mathematica, Tome 24 (2019), pp. 2381-2422
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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 Zp​(r). We show that our conjecture is essentially equivalent to the p-part of the equivariant Tamagawa number conjecture for the pair (h0(Spec(L))(r),Z[G]). We derive from this explicit constraints on the Galois module structure of Banaszak's p-adic wild kernels.
DOI : 10.4171/dm/728
Classification : 11R42, 11R70, 19F27
Mots-clés : K-theory, wild kernels, equivariant Tamagawa number conjecture, special L-values, Schneider's conjecture, annihilation 
@article{10_4171_dm_728,
     author = {Andreas Nickel},
     title = {Annihilating {Wild} {Kernels}},
     journal = {Documenta mathematica},
     pages = {2381--2422},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/728},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/728/}
}
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Andreas Nickel. Annihilating Wild Kernels. Documenta mathematica, Tome 24 (2019), pp. 2381-2422. doi: 10.4171/dm/728

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