Title: On the First Galois Cohomology Group of the Algebraic Group SL<sub>1</sub>(<i>D</i>)
Abstract: Let A be a central simple algebra over a field F. Denote the reduced norm of A over F by Nrd: A* → F* and its kernel by SL1(A). For a field extension K of F, we study the first Galois Cohomology group H 1(K,SL1(A)) by two methods, valuation theory for division algebras and K-theory. We shall show that this group fails to be stable under purely transcendental extension and formal Laurent series.
Publication Year: 2008
Publication Date: 2008-01-25
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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