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Iwasawa $λ$ invariant and Massey product

Peikai Qi

Abstract

We compute Iwasawa $λ$ invariant in terms of Massey products in Galois cohomology with restricted ramification. When applied to imaginary quadratic fields and cyclotomic fields, we obtain a new proof and generalization of results of Gold and McCallum-Sharifi. The main tool is the generalized Bockstein map introduced by Lam-Liu-Sharifi-Wake-Wang.

Iwasawa $λ$ invariant and Massey product

Abstract

We compute Iwasawa invariant in terms of Massey products in Galois cohomology with restricted ramification. When applied to imaginary quadratic fields and cyclotomic fields, we obtain a new proof and generalization of results of Gold and McCallum-Sharifi. The main tool is the generalized Bockstein map introduced by Lam-Liu-Sharifi-Wake-Wang.
Paper Structure (17 sections, 35 theorems, 118 equations)

This paper contains 17 sections, 35 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. Background
  3. The strategy and notations
  4. Main theorem and corollaries
  5. Structure of the paper
  6. Generalized Bockstein map and Massey product
  7. Generalized Bockstein map
  8. Massey product
  9. Size of $H^2$
  10. Applications to number theory
  11. Application to concrete examples
  12. Imaginary Quadratic field
  13. case 1
  14. numerical criterion
  15. case 2
  16. ...and 2 more sections

Key Result

Theorem 1

Let $K\subset K_1\subset K_2\subset \cdots \subset K_\infty$ be a $\mathbb{Z}_p$ extension of $K$ and $S$ be the set of primes above $p$ for $K$. Assume all primes in $S$ are totally ramified in $K_\infty/K$. Let $X_{cs}=\varprojlim\mathrm{Cl}_S(K_l)$ and $\mu_{cs}$, $\lambda_{cs}$ be the Iwasawa in

Theorems & Definitions (87)

  • Theorem 1
  • Theorem 2
  • Remark 1
  • Remark 2
  • Theorem 3
  • Remark 3
  • Theorem 4: Theorem A in LLSWWMR4537772
  • Lemma 5
  • proof
  • Proposition 1
  • ...and 77 more