The Essential Dimension of Central Simple Algebras

2015 ◽  
pp. 561-584
Author(s):  
Jean-Pierre Tignol ◽  
Adrian R. Wadsworth
Keyword(s):  
Essential Dimension ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

scholarly journals Essential dimension of central simple algebras

2012 ◽  
Vol 209 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Sanghoon Baek ◽  
Alexander S. Merkurjev
Keyword(s):  
Essential Dimension ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

scholarly journals Essential Dimension, Symbol Length and -rank

2020 ◽  
Vol 63 (4) ◽  
pp. 882-890
Author(s):  
Adam Chapman ◽  
Kelly McKinnie
Keyword(s):  
Lower Bounds ◽  
Cohomology Group ◽  
Upper And Lower Bounds ◽  
Essential Dimension ◽  
Base Field ◽  
Central Simple Algebras ◽  
Simple Algebras ◽  
Central Simple

AbstractWe prove that the essential dimension of central simple algebras of degree $p^{\ell m}$ and exponent $p^{m}$ over fields $F$ containing a base-field $k$ of characteristic $p$ is at least $\ell +1$ when $k$ is perfect. We do this by observing that the $p$-rank of $F$ bounds the symbol length in $\text{Br}_{p^{m}}(F)$ and that there exist indecomposable $p$-algebras of degree $p^{\ell m}$ and exponent $p^{m}$. We also prove that the symbol length of the Kato-Milne cohomology group $\text{H}_{p^{m}}^{n+1}(F)$ is bounded from above by $\binom{r}{n}$ where $r$ is the $p$-rank of the field, and provide upper and lower bounds for the essential dimension of Brauer classes of a given symbol length.

Locally Finite Central Simple Algebras

2021 ◽  
Author(s):  
Tamar Bar-On ◽  
Shira Gilat ◽  
Eliyahu Matzri ◽  
Uzi Vishne
Keyword(s):  
Central Simple Algebras ◽  
Locally Finite ◽  
Simple Algebras ◽  
Central Simple
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