On the Trace Map between Absolutely Abelian Number Fields of Equal Conductor
نویسنده
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.
منابع مشابه
On the Trace Map between Abelian Number Fields of Equal Conductor
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 [4]. The explicit nature of the calculations used to compute I(L/K) leads to the...
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