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Local Units Modulo Gauss Sums

✍ Scribed by Humio Ichimura

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 432 KB
Volume: 68
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2206

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✦ Synopsis

For a prime number p and a number field k, let k Âk be the cyclotomic Z p -extension. Let A be the projective limit of the p-part of the ideal class group of each intermediate field of k Âk. When k is totally real, it is conjectured that A is finite, namely that the characteristic polynomial char(A ) of A as a 4-module is 1. We give an interpretation of char(A ) (and hence, of the conjecture) in terms of p-adic behaviour of certain Gauss sums when k is a real abelian field (satisfying some conditions). When k=Q(cos(2?Âp)), similar results are already obtained by Coleman [3], Kaneko and the author [9].

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