Nickel, Andreas (2011) Leading terms of Artin L-series at negative integers and annihilation of higher K-groups. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 151. pp. 1-22. ISSN 0305-0041, 1469-8064
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Let L/K be a finite Galois extension of number fields with Galois group G. We use leading terms of Artin L-series at strictly negative integers to construct elements which we conjecture to lie in the annihilator ideal associated to the Galois action on the higher dimensional algebraic K-groups of the ring of integers in L. For abelian G our conjecture coincides with a conjecture of Snaith and thus generalizes also the well-known Coates-Sinnott conjecture. We show that our conjecture is implied by the appropriate special case of the equivariant Tamagawa number conjecture (ETNC) provided that the Quillen-Lichtenbaum conjecture holds. Moreover, we prove induction results for the ETNC in the case of Tate motives h(0) (Spec (L))(r), where r is a strictly negative integer. In-particular, this implies the ETNC for the pair (h(0)(Spec (L))(r), (sic), where L is totally real, r < 0 is odd and (sic) is a maximal order containing Z[1/2]G, and will also provide some evidence for our conjecture.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BLOCH-KATO CONJECTURE; GALOIS STRUCTURE; VALUES; UNITS; RINGS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 09 Jun 2020 05:49 |
| Last Modified: | 09 Jun 2020 05:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20620 |
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