Geodesic
The vanishing of Iwasawa's $\mu$-invariant implies the weak Leopoldt conjecture
Documenta mathematica, Tome 27 (2022), pp. 2275-2299 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Let K denote a number field containing a primitive p-th root of unity; if p=2, then we assume K to be totally imaginary. If K∞​/K is a Zp​-extension such that no prime above p splits completely in K∞​/K, then the vanishing of Iwasawa's invariant μ(K∞​/K) implies that the weak Leopoldt Conjecture holds for K∞​/K. This is actually known due to a result of Ueda, which appears to have been forgotten. We present an elementary proof which is based on a reflection formula from class field theory.
DOI : 10.4171/dm/x29
Classification : 11R23
Mots-clés : class field theory, reflection formula, weak Leopoldt conjecture, Iwasawa μ-invariant, uniform p-adic Lie extension, p-adic Galois representation 
@article{10_4171_dm_x29,
     author = {S\"oren Kleine},
     title = {The vanishing of {Iwasawa's} $\mu$-invariant implies the weak {Leopoldt} conjecture},
     journal = {Documenta mathematica},
     pages = {2275--2299},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x29},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x29/}
}
TY  - JOUR
AU  - Sören Kleine
TI  - The vanishing of Iwasawa's $\mu$-invariant implies the weak Leopoldt conjecture
JO  - Documenta mathematica
PY  - 2022
SP  - 2275
EP  - 2299
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x29/
DO  - 10.4171/dm/x29
ID  - 10_4171_dm_x29
ER  - 
%0 Journal Article
%A Sören Kleine
%T The vanishing of Iwasawa's $\mu$-invariant implies the weak Leopoldt conjecture
%J Documenta mathematica
%D 2022
%P 2275-2299
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x29/
%R 10.4171/dm/x29
%F 10_4171_dm_x29
Sören Kleine. The vanishing of Iwasawa's $\mu$-invariant implies the weak Leopoldt conjecture. Documenta mathematica, Tome 27 (2022), pp. 2275-2299. doi: 10.4171/dm/x29

Cité par Sources :