This version contains several important error corrections: more particularly, the proof of FLT first case given in preprint 333 has has been removed. In an other part, it improves significantly results of preprint 333 on class group (chapter 6), unit group (chapter 7) and Hilbert's class field (chapter 9) of the cyclotomic field $\Q(\zeta_p)$.

The proofs rest on classical elementary theory of the cyclotomic number field $\Q(zeta_p)$ and of representations of $Gal(\Q(\zeta_p)/\Q)$.

- fd20618.dvi (798836 bytes) [2002 Jul 16]
- fd20618.dvi.gz (255443 bytes)
- fd20618.ps.gz (524120 bytes)

Roland Queme <roland.queme@free.fr>