On the /-adic Iwasawa ¿-invariant in a //-extension
نویسندگان
چکیده
For distinct primes / and p , the Iwasawa invariant XT stabilizes in the cyclotomic Zp -tower over a complex abelian base field. We calculate this stable invariant for p = 3 and various / and K. Our motivation was to search for a formula of Riemann-Hurwitz type for XT that might hold in a p-extension. From our numerical results, it is clear that no formula of such a simple kind can hold. In the course of our calculations, we develop a method of computing XT for an arbitrary complex abelian field and, for p = 3 , we make effective Washington's theorem on the stabilization of the /-part of the class group in the cyclotomic Zp-extension. A new proof of this theorem is given in the appendix.
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