The main conjecture of Iwasawa theory for totally real fields
نویسندگان
چکیده
منابع مشابه
Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases
Fix an odd prime p. Let G be a compact p-adic Lie group containing a closed, normal, pro-p subgroup H which is abelian and such that G/H is isomorphic to the additive group of p-adic integers Zp. First we assume that H is finite and compute the Whitehead group of the Iwasawa algebra, Λ(G), of G. We also prove some results about certain localisation of Λ(G) needed in Iwasawa theory. Let F be a t...
متن کاملOn the “main Conjecture” of Equivariant Iwasawa Theory
The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...
متن کاملOn the “main Conjecture” of Equivariant Iwasawa Theory
The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...
متن کاملOn the Equivariant Main Conjecture of Iwasawa Theory
Refining results of David Burns and Cornelius Greither, respectively Annette Huber and Guido Kings, we formulate and prove an equivariant version of the main conjecture of Iwasawa theory for abelian number fields.
متن کاملIWASAWA THEORY OF TOTALLY REAL FIELDS FOR CERTAIN NON-COMMUTATIVE p-EXTENSIONS
In this paper, we prove the Iwasawa main conjecture (in the sense of [CFKSV]) of totally real fields for certain specific noncommutative p-adic Lie extensions, using the integral logarithms introduced by Oliver and Taylor. Our result gives certain generalization of Kato’s proof of the main conjecture for Galois extensions of Heisenberg type ([Kato1]). 0. Introduction 0.
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2012
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-012-0436-x