On the Trace Map between Absolutely Abelian Number Fields of Equal Conductor

نویسنده

  • HENRI JOHNSTON
چکیده

After first determining criteria for wild ramification of L/K (which can only happen at primes above 2), the above result is obtained for n = 2 (e ≥ 3) by computing TL/K(OL) explicitly, and is then extended to the general case. This approach does not rely on Leopoldt’s Theorem, in contrast to the techniques used in [6]. The explicit nature of the calculations used to compute I(L/K) leads to the definition of an “adjusted trace map” T̂Q(n)/K with the property that T̂Q(n)/K(O) = OK (here Q denotes the n cyclotomic field and O(n) its ring of integers). Using this map, we restate Leopoldt’s Theorem and show that its proof can be reduced to the (easier) cyclotomic case.

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تاریخ انتشار 2006