The lifted root number conjecture for small sets of places
- Autores: A. Nickel
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 2, 2009, págs. 446-470
- Idioma: inglés
- DOI: 10.1112/jlms/jdp036
- Enlaces
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Resumen
Let L/K be a finite Galois extension of number fields with Galois group G. The lifted root number conjecture (LRNC) by Gruenberg, Ritter and Weiss relates the leading terms at zero of Artin L-functions attached to L/K to natural arithmetic invariants. Burns used complexes arising from �Letale cohomology of the constant sheaf Z to define a canonical element T�¶(L/K) of the relative K-group K0(ZG,R). It was shown that the LRNC for L/K is equivalent to the vanishing of T�¶(L/K) and that this, in turn, is equivalent to the equivariant Tamagawa number conjecture for the pair (h0(Spec(L))(0), ZG). These conjectures make use of a finite G-invariant set S of places of L that is supposed to be sufficiently large. We formulate an LRNC for small sets S that only need to contain the archimedean primes and give an application to a special class of CM-extensions.
