Greenberg's conjecture and cyclotomic towers
نویسندگان
چکیده
منابع مشابه
Cyclotomic Units and the Iwasawa Main Conjecture
In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...
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Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
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We give new examples of real quadratic fields k for which the Iwasawa invariant λ3(k) and μ3(k) are both zero by calculating cyclotomic units of real cyclic number fields of degree 18.
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the cyclotomic Iwasawa algebra of ”tame level m0”. Using étale cohomology one can define a certain perfect complex of Λ-modules ∆∞ (see section 1.2 below) and a certain basis L of the invertible Q(Λ)-module DetQ(Λ)(∆∞⊗Λ Q(Λ)) where Q(Λ) is the total ring of fractions of Λ. This basis L is obtained by l-adically interpolating the leading Taylor coefficients of the Dirichlet L-functions L(χ, s) a...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2004
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa113-1-1