Iwasawa Theory of Local Units

Abstract

Iwasawa [Iw 8], [Iw 10] developed a theory of local units analogous to the global theory, taking projective limits, especially in the cyclotomic tower, and getting the structure of this projective limit modulo the closure of the cyclotomic units. He considers eigenspaces for the characters of Gal(K₀/Q _p ) where K₀ = Q _p (ζ) with a primitive pth root of unity ζ. Since the cyclotomic units are essentially real, we consider only even non-trivial characters. Then the eigen-space is isomorphic to Λ/(g), where g is a power series which is essentially the p-adic L-function.