Units and Cyclotomic Units in Zp-Extensions
نویسندگان
چکیده
منابع مشابه
Cyclotomic Units and Class Groups in Zp-extensions of real abelian fields
For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic Zp-extension of F . Assuming Greenberg’s conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomo...
متن کاملGREENBERG'S CONJECTURE AND UNITS IN MULTIPLE Zp-EXTENSIONS
Let A be the inverse limit of the p-part of the ideal class groups in a Zpextension K∞/K. Greenberg conjectures that if r is maximal, then A is pseudo-null as a module over the Iwasawa algebra Λ (that is, has codimension at least 2). We prove this conjecture in the case that K is the field of p-th roots of unity, p has index of irregularity 1, satisfies Vandiver’s conjecture, and satisfies a mi...
متن کاملL-functions and Cyclotomic Units
Here RK is the regulator of K, wK is the number of roots of unity in K and hK is the class number of K. This formula is a striking connection between arithmetic and analysis, and there have been many attempts to generalize it to other L-functions: one expects that the value of a “motivic” L-function at an integer point should involve a transcendental factor, a boring rational factor, and an int...
متن کاملCyclotomic 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...
متن کاملCyclotomic units and Greenberg's conjecture for real quadratic fields
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1995
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000005432