The T and T∗ components of Λ - modules and Leopoldt's conjecture. (arXiv:0905.1274v3 [math.NT] UPDATED)

arXivを（Google reader経由で）見ていたら，Leopoldt予想を一般に解決したとするプレプリントを発見した．
著者はCatalan予想を解決したP. Mihailescu. 詳細は後日に譲るとして，とりあえず速報でした．

The $T$ and $T^{\ast }$ components of $\mathrm{\Lambda }$ - modules and Leopoldt's conjecture. (arXiv:0905.1274v3 [math.NT] UPDATED):

"The conjecture of Leopoldt states that the $p$ - adic regulator of a number field does not vanish. It was proved for the abelian case in 1967 by Brumer, using Baker theory. A conjecture, due to Gross and Kuz'min will be shown here to be in a deeper sense a dual of Leopoldt's conjecture with respect to the Iwasawa involution. We prove both conjectures for arbitrary number fields $\text{K}$.
The main ingredients of the proof are the Leopoldt reflection, the structure of quasi - cyclic ${\text{Z}}_p[\text{Gal}(\text{K}/\text{Q})]$ - modules of some of the most important $\mathrm{\Lambda }[\text{Gal}(\text{K}/\text{Q})]$ - modules occurring ($T$ acts on them like a constant in ${\text{Z}}_p$), and the Iwasawa skew symmetric pairing."