Formulation
Iwasawa worked with so-called -extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a -extension is the same thing as a tower of fields such that . Iwasawa studied classical Galois modules over by asking questions about the structure of modules over .
More generally, Iwasawa theory asks questions about the structure of Galois modules over extensions with Galois group a p-adic Lie group.
Read more about this topic: Iwasawa Theory
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