Consequences of Kida's Formula for Non-Primitive Iwasawa Modules
by
Alexandra Nichifor
University of Washington

Kida's formula indicates how the lambda-invariants of the minus parts of the classical Iwasawa modules are related in p-extensions of CM number fields, in terms of ramification indices and the degree of the field extension.

This talk will describe a non-primitive version of Kida's formula and will show how it can be used to study the module structure of the corresponding non-primitive Iwasawa module. As a consequence, the characteristic polynomial of the non-primitive Selmer group of certain elliptic curves with good ordinary reduction at an odd prime p and with rational isogenies of degree p² is interpreted, modulo p², in terms of the characteristic polynomials of certain non-primitive classical Iwasawa modules.

Date received: May 27, 2004