Iwasawa Descent and Co-descent for Units modulo Circular Units

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O ct 2 00 6 Global Units modulo Circular Units : descent without Iwasawa ’ s Main Conjecture . ∗

Iwasawa’s classical asymptotical formula relates the orders of the p-parts Xn of the ideal class groups along a Zp-extension F∞/F of a number field F , to Iwasawa structural invariants λ and μ attached to the inverse limit X∞ = lim ← Xn. It relies on ”good” descent properties satisfied by Xn. If F is abelian and F∞ is cyclotomic it is known that the p-parts of the orders of the global units mod...

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Global Units modulo Circular Units : descent without Iwasawa’s Main Conjecture

Iwasawa’s classical asymptotical formula relates the orders of the p-parts Xn of the ideal class groups along a Zp-extension F∞/F of a number field F , to Iwasawa structural invariants λ and μ attached to the inverse limit X∞ = lim ← Xn. It relies on ”good” descent properties satisfied by Xn. If F is abelian and F∞ is cyclotomic it is known that the p-parts of the orders of the global units mod...

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2 4 M ay 2 00 6 Global Units modulo Circular Units : descent without Iwasawa ’ s Main Conjecture . ∗

Iwasawa’s classical asymptotical formula relates the orders of the p-parts Xn of the ideal class groups along a Zp-extension F∞/F of a number field F , to Iwasawa structural invariants λ and μ attached to the inverse limit X∞ = lim ← Xn. It relies on ”good” descent properties satisfied by Xn. If F is abelian and F∞ is cyclotomic it is known that the p-parts of the order of the global units modu...

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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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ژورنال

عنوان ژورنال: Pure and Applied Mathematics Quarterly

سال: 2006

ISSN: 1558-8599,1558-8602

DOI: 10.4310/pamq.2006.v2.n2.a4