Preda Mihailescu (Goettingen)
Lambda - Modules and the Iwasawa skew symmetric pairing
Abstract:
We give an explicit description of the structure of Z_p - free Lambda -
torsion modules M (Weierstrass modules), which determines the growth of the
intermediate level modules, in the case when M is a projective limit. This way we define
Kummer pairings above cyclotomic Z_p extensions, as projective - projective
pairings and obtain an alternative description of Iwasawa's skew symmetric pairing.
This aparatus shows useful for the proof of two imporant conjectures in Iwasawa theory,
the conjecture of Leopoldt and the one of Gross - Kuz'min. We give a sketch of the main
steps of these proofs.