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

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Castillo H., Jones A.

Acta Arithmetica

2013

tom 160

nr 1

67-93

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.

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1 Acta Arithmetica

1 Castillo H.

1 Jones A.

1 2013

Wyniki wyszukiwania

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