Embeddings of fields in simple algebras over global fields

2011/08/03 by Sheng-Chi Shih, Shih, Sheng-Chi, Tse-Chung Yang +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1108.0830

openalex publication_date 2011/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a global field, A a central simple algebra over F and K a finite (separable or not) field extension of F with degree [K:F] dividing the degree of A over F. An embedding of K in A over F exists implies an embedding exists locally everywhere. In this paper we give detailed discussions when the converse (i.e. the local-global principle in question) may hold.

Cited by

• Epsilon dichotomy via root numbers of intertwining periods

Related

• Embeddings of local fields in simple algebras and simplicial structures on the Bruhat-Tits building
• Integral embeddings of central simple algebras over number fields
• Extensions of locally matricial and locally semisimple algebras
• Local-global principles for embedding of fields with involution into simple algebras with involution
• Strong linkage for function fields of surfaces