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

• Andreas Nickel ^[1]
  1. [1] University of Duisburg-Essen

     University of Duisburg-Essen

     Kreisfreie Stadt Essen, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
• Idioma: inglés
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• Resumen

  • Let 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 be an odd integer. The p-adic Beilinson conjecture relates the values at 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 (h0(Spec(E))(r),Z[G]). If r>1 is even we obtain a similar result for Galois CM-extensions after restriction to ‘minus parts’.