How does Iwasawa theory relate to cyclotomic fields?

Iwasawa theory is a branch of number theory that studies the arithmetic properties of cyclotomic fields. These fields are extensions of the rational numbers obtained by adding roots of unity, which are complex numbers that satisfy a certain algebraic equation. Iwasawa theory provides a framework for understanding the behavior of certain arithmetic invariants of these fields, such as the class numbers and the structure of the ideal class group. By studying the relationships between these invariants as the cyclotomic field varies, Iwasawa theory sheds light on the deeper connections between number theory and algebraic geometry.

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