On index-exponent relations over Henselian fields with local residue\n fields

2014/01/09 by Ivan D. Chipchakov, Chipchakov, Ivan D.
Mathematics · #11S99 #12E15 #12J10 (primary) #13F30 (secondary) #16K50 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1401.2005

openalex publication_date 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and (K, v) a Henselian valued field with a\nresidue field widehat K. This paper determines the Brauer p-dimension of\nK, in case p \≠ rm char( widehat K) and widehat K is a\np-quasilocal field properly included in its maximal p-extension. When\n widehat K is a local field, it describes index-exponent pairs of central\ndivision K-algebras of p-primary degrees. The same goal is achieved, if\n(K, v) is maximally complete, char(K) = p and widehat K is local.\n

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