On the equivariant Tamagawa number conjecture for Tate motives and unconditional annihilation results
Johnston, Henri; Nickel, Andreas
Date: 20 August 2015
Article
Journal
Transactions of the American Mathematical Society
Publisher
American Mathematical Society
Publisher DOI
Abstract
Let L/K be a finite Galois extension of number fields with Galois
group G. Let p be a prime and let r ≤ 0 be an integer. By examining
the structure of the p-adic group ring Zp[G], we prove many new cases of
the p-part of the equivariant Tamagawa number conjecture (ETNC) for the
pair (h0(Spec(L))(r), Z[G]). The same methods can also ...
Let L/K be a finite Galois extension of number fields with Galois
group G. Let p be a prime and let r ≤ 0 be an integer. By examining
the structure of the p-adic group ring Zp[G], we prove many new cases of
the p-part of the equivariant Tamagawa number conjecture (ETNC) for the
pair (h0(Spec(L))(r), Z[G]). The same methods can also be applied to other
conjectures concerning the vanishing of certain elements in relative algebraic
K-groups. We then prove a conjecture of Burns concerning the annihilation
of class groups as Galois modules for a large class of interesting extensions,
including cases in which the full ETNC is not known. Similarly, we construct
annihilators of higher dimensional algebraic K-groups of the ring of integers
in L.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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