Contents Online
Asian Journal of Mathematics
Volume 18 (2014)
Number 2
Embeddings of fields into simple algebras over global fields
Pages: 365 – 386
DOI: https://dx.doi.org/10.4310/AJM.2014.v18.n2.a9
Authors
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 $K$ into $A$ over $F$ exists implies an embedding exists locally everywhere. In this paper we give detailed discussions about when the converse (i.e. the local-global principle in question) may hold.
Keywords
central simple algebras, embeddings, the Hasse principle, Galois cohomology
2010 Mathematics Subject Classification
11E72, 17C20
Published 13 May 2014