Kida's formula via Selmer complexes

TL;DR

This paper introduces a new approach to Kida's formula in Iwasawa theory using Selmer complexes, providing a unified perspective on the behavior of arithmetic invariants under field extensions.

Contribution

It presents a novel method leveraging Selmer complexes to derive analogues of Kida's formula, advancing the theoretical framework in Iwasawa theory.

Findings

New perspective on Kida's formula via Selmer complexes

Unified approach applicable to various Iwasawa invariants

Potential for broader generalizations in arithmetic modules

Abstract

In Iwasawa theory, the $\lambda$, $\mu$-invariants of various arithmetic modules are fundamental invariants that measure the size of the modules. Concerning the minus components of the unramified Iwasawa modules, Kida proved a formula that describes the behavior of those invariants with respect to field extensions. Subsequently, many analogues of Kida's formula have been found in various areas in Iwasawa theory. In this paper, we present a novel approach to such analogues of Kida's formula, based on the perspective of Selmer complexes.