Cohomological invariants of central simple algebras

2016 ◽  
Vol 80 (5) ◽  
pp. 869-883 ◽  
Author(s):  
A S Merkurjev
Keyword(s):  
Central Simple Algebras ◽  
Cohomological Invariants ◽  
Simple Algebras ◽  
Central Simple

scholarly journals Invariants of degree 3 and torsion in the Chow group of a versal flag

2015 ◽  
Vol 151 (8) ◽  
pp. 1416-1432 ◽  
Author(s):  
Alexander Merkurjev ◽  
Alexander Neshitov ◽  
Kirill Zainoulline
Keyword(s):  
Algebraic Group ◽  
Chow Group ◽  
Linear Algebraic Group ◽  
Factor Group ◽  
Central Simple Algebras ◽  
Cohomological Invariants ◽  
Simple Algebras ◽  
Central Simple ◽  
Torsion Part

We prove that the group of normalized cohomological invariants of degree $3$ modulo the subgroup of semidecomposable invariants of a semisimple split linear algebraic group $G$ is isomorphic to the torsion part of the Chow group of codimension-$2$ cycles of the respective versal $G$-flag. In particular, if $G$ is simple, we show that this factor group is isomorphic to the group of indecomposable invariants of $G$. As an application, we construct nontrivial cohomological invariants for indecomposable central simple algebras.

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