On the p-adic Beilinson conjecture and the equivariant Tamagawa number conjecture

Abstract

AbstractLet E/K be a finite Galois extension of totally real number fields with Galois group G. Let p be an odd prime and let $$r>1$$ r > 1 be an odd integer. The p-adic Beilinson conjecture relates the values at $$s=r$$ s = r of p-adic Artin L-functions attached to the irreducible characters of G to those of corresponding complex Artin L-functions. We show that this conjecture, the equivariant Iwasawa main conjecture and a conjecture of Schneider imply the ‘p-part’ of the equivariant Tamagawa number conjecture for the pair $$(h^0(\mathrm {Spec}(E))(r), \mathbb {Z}[G])$$ ( h 0 ( Spec ( E ) ) ( r ) , Z [ G ] ) . If $$r>1$$ r > 1 is even we obtain a similar result for Galois CM-extensions after restriction to ‘minus parts’.