On the values of Artin L-series at s=1 and annihilation of class groups

• Autorzy: Hugo Castillo , Andrew Jones
• Języki publikacji: EN

Abstrakty

EN

Let L be a finite Galois CM-extension of a totally real field K. We show that the validity of an appropriate special case of the Equivariant Tamagawa Number Conjecture leads to a natural construction for each odd prime p of explicit elements in the (non-commutative) Fitting invariants over $ℤ_p[G]$ of a certain tame ray class group, and hence also in the analogous Fitting invariants of the p-primary part of the ideal class group of L. These elements involve the values at s=1 of the Artin L-series of characters of the group Gal(L/K). We also show that our results become unconditional under certain natural hypotheses on the extension L/K and prime p.

Kategorie tematyczne

• 11G40: L -functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 160
• Numer: 1
• Strony: 67-93

Daty

wydano

2013

Twórcy

autor

Hugo Castillo

• Department of Mathematics, King's College London, Strand WC2R 2LS, United Kingdom

autor

Andrew Jones

• 1 Sheridan Grove, Milton Keynes MK4 4GP, United Kingdom

Identyfikatory

DOI

10.4064/aa160-1-5