## Speaker:

Ralph Greenberg

## Speaker Link:

## Institution:

University of Washington

## Time:

Tuesday, May 3, 2016 - 2:00pm to 3:00pm

## Location:

RH 340P

There is a classical theorem of Iwasawa which concerns certain modules *X* for the formal power series ring Λ = **Z***p*[[T]] in one variable. Here *p* is a prime and **Z***p* is the ring of *p*-adic integers. Iwasawa's theorem asserts that *X* has no nonzero, finite Λ-submodules. We will begin by describing the modules *X* which occur in Iwasawa's theorem and explaining how the theorem is connected with the title of my talk. Then we will describe generalizations of this theorem for certain Λ-modules (the so-called "Selmer groups") which arise naturally in Iwasawa theory. The ring Λ can be a formal power series ring over **Z***p* in any number of variables, or even a non-commutative analogue of such a ring.