Exceptional case of the non semi-simple Real Abelian Main Conjecture

2023/08/09 by Georges Gras, Gras, Georges
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2308.04764

openalex publication_date 2023/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the papers: "The Chevalley--Herbrand formula and the real abelian Main Conjecture (New criterion using capitulation of the class group),J. Number Theory 248 (2023)" and "On the real abelian main conjecture in the non semi-simple case, arXiv (2023)", we consider real cyclic fields K and primes ℓ ≡ 1 \pmod 2p^N totally inert in K, implying implicitly, K ∩ ℚ(μ_p^∞)⁺ = ℚ. In this complementary work, we examine the non linearly disjoint case.

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