✦ LIBER ✦
Unités semi-locales modulo sommes de Gauss
✍ Scribed by Tatiana Beliaeva
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 309 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
For an odd prime number p and an abelian number field k, let k ∞ /k be the cyclotomic Z p -extension. Let X ∞ be the projective limit of the p-parts of the ideal class groups of each intermediate field of k ∞ /k. It is conjectured (Greenberg's Conjecture) that X ∞ is finite when k is totally real. In this paper we give an interpretation of the characteristic polynomial of X ∞ in terms of certain Gauss sums. We also give analogous results at finite level. Our results generalize those obtained by Ichimura (