• 1 Introduction ▶
    • 1.1 Iwasawa’s theorem on growth of class groups
  • 2 Preliminaries in commutative algebra ▶
    • 2.1 Random
    • 2.2 Noetherian integrally closed domain
    • 2.3 Semilocal PID
  • 3 Structure of module up to pseudo-isomorphism ▶
    • 3.1 Characteristic ideal
    • 3.2 Pseudo-null module
    • 3.3 Structure theorem
    • 3.4 Noetherian regular domain
  • 4 Structure of Iwasawa module ▶
    • 4.1 Iwasawa algebra
    • 4.2 Weierstrass preparation theorem
    • 4.3 Characteristic ideal
    • 4.4 Growth of coinvariant part
  • 5 Arithmetic of \({\mathbb {Z}}_p\)-extensions ▶
    • 5.1 The class group of \({\mathbb {Z}}_p\)-extension of a number field
    • 5.2 Recover the finite level of class group from infinite level
  • A Known results in mathlib ▶
    • A.1 Rings
    • A.2 Ideals
    • A.3 Modules
    • A.4 Number theory
  • Dependency graph

Formalization of Iwasawa Theory in LꓱꓯN

Jz Pan

  • 1 Introduction
    • 1.1 Iwasawa’s theorem on growth of class groups
  • 2 Preliminaries in commutative algebra
    • 2.1 Random
    • 2.2 Noetherian integrally closed domain
    • 2.3 Semilocal PID
  • 3 Structure of module up to pseudo-isomorphism
    • 3.1 Characteristic ideal
    • 3.2 Pseudo-null module
    • 3.3 Structure theorem
    • 3.4 Noetherian regular domain
  • 4 Structure of Iwasawa module
    • 4.1 Iwasawa algebra
    • 4.2 Weierstrass preparation theorem
    • 4.3 Characteristic ideal
    • 4.4 Growth of coinvariant part
  • 5 Arithmetic of \({\mathbb {Z}}_p\)-extensions
    • 5.1 The class group of \({\mathbb {Z}}_p\)-extension of a number field
    • 5.2 Recover the finite level of class group from infinite level
  • A Known results in mathlib
    • A.1 Rings
    • A.2 Ideals
    • A.3 Modules
    • A.4 Number theory